My Volvo S60 does not require premium gas…at all. Plain old regular.
When I’ve gotten the small Volvo suv as a loaner car, I was told regular was fine too.
Audi takes premium.
I have a Toyota RAV4 hybrid. It’s a compact SUV. I love it.
I would also look at the Lexus NX hybrid.
Another vote for Mercedes here. I had a ML that I put almost 200k hard miles in. Towing, road trips - it was a great machine. Quiet and super comfy. I could drive it 24 hours towing my boat and not feel fatigued. When my mechanic told me it was time for a new vehicle almost 2 years ago, I got the comparable Lexus (GX460) aiming for reliability. It’s reliable all right but now I’m like that classic Meatloaf song where I’m waiting ‘till the end of time… the Lexus sucks compared to the Mercedes in every single way except reliability. And both use premium gas.
For quiet comfort, get the Mercedes. If you don’t need an SUV a 3 year old E class is a bargain; 50% of the new price and a great, solid, quiet car. Not as reliable as the Lexus, though.
Can’t get any more quieter than an electric vehicle. BMW i3 is quicker than most anything out there. Chevy Bolt has the range of a Tesla but less expensive.
Lower end Lexus cars do not need premium. GX is a behemoth… very tank like. And definitely does not fall within OP’s criteria. 
NX, OTOH, is quite compact for an SUV.
Some older model Priuses came with Goodyear Integrity tires that were not that good in wet braking or handling. https://www.tirerack.com/tires/tests/testDisplay.jsp?ttid=121 found the Goodyear Integrity tires to be the worst in wet (but best in dry) among various other low rolling resistance (good fuel economy) tires.
So it may be possible to upgrade the grip with a difference choice of tires. It is also possible that the current Prius comes with tires with significantly different performance characteristics from the tires that came on older Priuses.
I have an Audi S4 and love, love it. The tires make a huge difference in the amount of road noise. It has variable settings for drive feel and can go from a comfort to a sport setting easily. The A6 I had prior to this car was definitely more luxe and comfort; the S4 is definitely a driver’s car and is more sport-tuned.
Yes, it takes premium, but most “luxury” cars do, including my sister’s Lexus and my husband’s Infinity. So did my VW and my Subaru for that matter. I buy fuel from Costco, so the cost differential isn’t too bad.
I like my sister’s Lexus (I think it’s a 2014) - small, comfy, and enjoyable to ride in. Lots of features and extras.
Mid 30s to mid 40s will reduce your choice of new cars, but is well in the range for one a couple of years old.
Such solid and great information. You have made me realize that I need to enter the jungle and deal with the salespeople and test drive some of these cars. And thanks, chercheur, for the reminder that we can test drive it by ourselves. Our credit is frozen so at least they cannot run a credit check on us (as use to be protocol).
One of the things that put me off with the broker I spoke with is he did not give me a satisfactory answer when asked about his payment. Song and Danced away until I made it clear that I understood he was paid and needed to be paid. Finally, he said that he works that out with the seller/manufacturer. He goes to auction one time a month and, no doubt, can get great deals. The responses here have helped me realize that I did not like him and will not be using him. I will look into AAA and see how they are operating.
I do realize an electric car is the quietest. Recently a young friend with two children was to come over for dinner. She forgot to plug her car in and had no transportation. I would like a hybrid but not a car that is dependent on only electricity. I wonder what happens when we have our earthquake and there is no electricity for a long time. There might not be operating gas stations but more likely to be going again sooner. Of course there may not be many roads either (everyone in our family never goes below a half tank of gas). :-O.
I am clear I want a small car but will try some of the SUV’s. We just put the new G’son’s (two days late) new car seat base in and I wonder about lifting him up into an SUV (I am short). I do, also, love trunks. But driving both sedans and SUV’s sounds good. Plan to take the car seat base with us also. Need to comfortable fit baby and parents into backseat (Hyundai is great for this.
NJres, thanks for the laugh–am sure it is true that Lexus wants my money but not my admiration.
The gasoline pumps need electricity. Basically, if the electricity in your area goes out, you are not going to be refueling any kind of car (unless you have a portable can of gasoline to refuel a gasoline car). But you could drive the car to where the electricity is on and refuel it (at a public charging station if the car is electric).
Or you could install solar panels and batteries on your house to be able to have electricity without depending on the grid.
Good point about the electricity and the pumps. Gas stations are on main roads while homes are not.
And if you are completely out of electricity as my friend was then you cannot drive to a gas station.
Thanks, I do get your point. Still, I think a Hybrid would be great but not interested in an all electric.
Told H we need to double check our credit to be sure it is frozen and start visiting dealerships.
We need to be across town on Saturday in an area where every dealership brand in the world exists so guessing
we will walk (drive) the gantlet, so to speak.
A plug-in hybrid* would give you the ability to refuel from either an electric outlet or a gasoline pump.
*e.g. Chevrolet Volt, Honda Clarity PHEV, Chrysler Pacifica PHEV, etc…
^Thanks. Yes. H will not consider a the Chevy or the Chrysler.
Will check out the Honda Clarity.
Clarity is the size of an Accord 
. A size bigger than I want to go.
One of my neighbors just ordered the BMW 530e plug in hybrid. Apparently it’s just coming out.
We have a Hyundai Elantra, I get you on the noise. It has the worst road noise.
Just curious…what Subaru requires premium? We’ve owned three, including a current outback. None have required premium gas.
@oregon101 I was positive I didn’t want a Volvo, and drove a lot of cars. A lot. I agree that the only way you will know what is comfortable for you is to take the cars for a drive. As an example, my husband thinks the Accord is mighty comfortable. I don’t.
The other thing…make sure you look at some new models. Like i said, I was very pleased with the comfort and handling of a brand new Camry. Our family owns two (2012, and 2013) and they are fine…but this brand new one was wow comfortable…actually as comfy if not more so than my Volvo!
Other plug-in hybrids include the plug-in hybrid versions of the Kia Niro and Hyundai Ioniq, as well as the Toyota Prius Prime. You may be able to find a leftover discontinued Ford C-Max Energi. There is also the Ford Fusion Energi, but that may be larger than you want.
It hasn’t been mentioned yet, but a car that really I’d really like is the Porsche Macan, Porsche’s smallest SUV. Used models are in your budget. But I don’t know how quiet they are.
I have a Mercedes GLA, it is the smallest SUV, built on a sedan chasis. It is very quiet and comfortable. My friends have a BMW x3 and it is very similar to mine.
Of all the SUVs, the Macan was by far my favorite to drive. It’s very quiet and handles like a sports car. My mechanic recommended the S as the most reliable of the Macans. If it towed more (tow limit is ridiculously low, think 1600 lbs) that’s what I would have gotten this last time. I’ve talked two of my friends into getting them, though. Porsche should start giving me a commission.
If you want quiet, if not silent, consider an electric car. Maybe a Prius or a Nissan Leaf. If you want to spend a bit more, consider a Tesla 3.