St. Augustine is great. We were there last year. If you can get arrangements made that would be great…but you are looking ON season for this year…that could be a challenge.
Sarasota is also nice.
Wow, was gone all day and came back to so many ideas to research! Thanks all! Southern CA sounds fun; we’ve never been, and that one received the best reaction from my son. We’ve done just Disney in FL so lots of recommendations to consider in other areas of the state. (Any Key West/Dry Tortugas fans?) We love Sedona but agree with the poster who said it would probably be too cold. Ditto Bermuda becuase I’m thinking I might not make it until April, lol. Surprised no one recommended Puerto Rico or the Caribbean. I thought there’d be a lot of suggestions for those. Off to do some research!
Puerto Rico has been hit by a series of earthquakes. 
Sadly, it may not be a good time to visit.
Two thumbs up for Southern CA. San Diego is a lot of FUN!
There have been a number of threads on San Diego in the last year on cc - agree that it hits most of your criteria. Although we can’t promise it will go over 70 degrees!
If you are really interested in the Keys, then I’ll go back to my earlier posts about B&Bs, restaurants, etc.
If you find a reasonable flight into Palm Beach airport, then consider Palm Beach Gardens or Jupiter, both just north of PB. I stayed in a suite in Jupiter for a very reasonable rate. This airport is much smaller than Miami or FtL.
You might like Sanibel Island (fly to Ft. Myers).
Many quick and easy flights into Tampa. You might like Siesta Key.
Guessing no one recommended the Caribbean because it is high season there, and flights/lodging will be $$$$.
Sometimes you can find relatively inexpensive (<$400) flights to Cancun from the Northeast and the roughlky 4 hour flight makes it closer than CA or Arizona. We love the area south of Cancun - beautiful beaches, amazing snorkeling and diving, swimming in cenotes, mayan ruins, Ziplining in the jungle, great Mexican food. There are cheap places to stay and eat all along the coast, and the temperatures should be north of 80 degrees pretty reliably.
We’re going to Oaxaca, Mexico in February where the temps should be lower 80’s during the day. Flights for 2 and Airbnb for 11 nights are coming in at around $1300. No beach nearby, but lots to do.
My AirBnB link was to a place in the Dominican Republic. 
We loved it (as did the others writing reviews), it was inexpensive, and for us there were non-stop flights from BWI with Southwest. The site still has openings in both Feb and March…
As for the Dry Tortugas, we loved our time there as well, but I think you’d have to enjoy travel as we do. We took the boat there with enough belongings to spend three nights camping. There’s no electric and the toilets are composting. Our kids were younger at the time and all three loved it too. We had two rules. #1 Don’t leave the island without us. #2 Always go swimming or snorkeling with a buddy. Aside from that they could explore as they wanted with the fort, the moat, the beach, etc. It was a blast. Not terribly long ago my youngest (now college grad) told me one of his favorite memories was watching the stars get erased from the sky one morning from a walk around the moat that he and I took (the only two awake at the time). It’s one of my favorite memories too, so knowing it’s shared has an extra special thought now.
But most folks (we know) don’t enjoy primitive camping and can’t live without the internet for a little bit. The boat there is a day trip and allows you to explore some. We used to hide out under the trees when the boat was in for its few hours listening to a lot of folks talk with our boys about how lucky they were to be staying there.
Key West isn’t our favorite TBH, but we do like some of the campgrounds and places farther north in the Keys. If you’re a snorkeler or diver there are some places like Biscayne NP outside of Miami (they have glass bottom boat tours too, though we’ve never taken one) and the state parks like Pennekamp and Bahia Honda, but the Tortugas is better.
We have some family friends in Reno who like to go to Scottsdale, AZ in the winter. They always have a great time. It’s also a great destination if you like Golf. They don’t play golf, but they have always found non-golf stuff to do. H and I spent a few days there and we had a great time. The musical instrument museum in Phoenix is amazing. H and I loved it! We also really enjoyed the Desert botanical garden.
If you like baseball, you could always go to Arizona for spring training. D’s boss likes to go on Golf trips to Arizona.
There is also tons of good hiking in the greater Phoenix area…and a great foodie scene…lots of terrific restaurants at every price point.
The MIM (Musical Instrument Museum) is a must see. Desert Botanical Gardens too…but go for a docent led tour…very well worth it!
@Creekland that airbnb looks awesome, but I’ve read crime is high in Dominican Republic. Maybe that is in the more touristy areas?? We are big campers, and lack of internet access doesn’t bother us, but I do like a plumbed bathroom with showers 
So many suggestions in FL. I’m trying to narrow it down to a few top choices. We don’t want anything built up with high rises, chain restaurants, and lots of traffic. Definitely want a quiet vibe but somewhere with character (nice architecture, interesting stores, towns to walk around, a museum or other cultural activity, great outdoor spaces and/or a beach to hike/explore/relax. Will continue doing research on the suggestions offered so far. My husband’s coworker suggested Sarasota - any input on that? I don’t think it’s been mentioned here yet.
I mentioned Sarasota. It has a nice downtown area. The circus museum is there and it’s really interesting.
We really liked St. Augustine…it was very nice. Lots to do. The tour of Flagler College and the history of the railroad there is really terrific. Neat little downtown area.
What about Amelia Island? That’s nice too.
We liked St. Augustine, too.
Thanks @thumper1 I somehow missed that when I was transcribing the recommendation to a Word doc. St. Augustine looks quite lovely too.
My go to Caribbean places for warm February travel are Grand Cayman and Turks and Caicos, but they are both likely above the price point mentioned during that time.
We heard about the high crime in the DR too, but that didn’t stop us from going. We never once felt unsafe where we were. I think the crime is mainly in the big cities and perhaps around the resorts. This place is in a small ex fishing village. The bus tourists in from the resorts daily to do excursions to the islands or enjoy the beach, etc, but then they ship them back out again at night. It was neat for us watching the whole process while leisurely walking where we wanted to go. Prices are also better once one gets away from the main cruise/bus location.
For FL, St Augustine is quite nice though you aren’t guaranteed warm that far north in FL. If you haven’t been to the Keys, I’d suggest that. It is fun to explore that area. I’m not sure what you will find in availability at a reasonable price.
“Lots of traffic” happens in FL in the winter, but if you stay away from the bigger cities it isn’t quite as bad though my uncle in Naples would disagree with me - bad is relative. If you head to the St Petersburg area, go to Ft Desoto county park for the “no high rise” bit. There are quite a few miles of beaches we walk there and they have flush toilets. We’ll be there ourselves (camping) for a bit of Feb, but the campground is probably full booked except for the last minute sites they release on Fridays. St Pete Beach itself has the high rises.
Other thoughts… Venice? (FL, not Italy) Some of the islands recommended might be too pricey and/or have lack of availability. Search a bit on AirBnB to see what’s still out there.
ps Grand Bahama can be inexpensive and has a little bit to explore. We spent a month there enjoying ourselves a few Februaries ago - though that was before the last two hurricanes went through. Stay near Lucaya, not Freeport. Freeport is dangerous. Lucaya didn’t seem to be, but we didn’t go out at night. Where we were in the DR night wasn’t really a problem.
The DR has actually had some very serious issues IN the high end resorts in the last year or so. Drinks have been spiked and there have been assaults, robberies and deaths resulting from this. Resort staff have been implicated in a number of the incidents.