Antrak has a freight service that works out to a very reasonable price, if you are both in areas amtrak serves.
No specific recommendation, but when a relative wanted a couple of boxes and small furniture items moved to his home from his parents’ home, he had great luck with websites where you could describe your items to movers with extra room on a truck and get bids for door to door delivery. It was a few years ago and worked well for him. Price was very reasonable. Of course, you want a way to assess the movers; not sure how that is built-in to the process.
The Army will move our son’s stuff to his first duty station when he graduates in May. It won’t be much more than a carful because w/he totally cleaned out his room when we downsized a few years ago and only moved some clothes, books, erg, and small electronics to the new place. He donated the erg to the ASU women’s rowing team a few months ago. He bought a car over the summer and is paying the storage fee because we don’t have room for it in our garage. Like @emilybee, I also have two big Tupperware bins with mementos from his childhood, but those are for me. It makes me sad how little of him is actually here, and I don’t want to think about that empty space after graduation. 
Amtrak lets you take quite a number of pieces of luggage (5 is what I recall per person) as check thru on the train. Transport the goods via Amtrak one way and fly back.
We still have a ton of our kids’ stuff. S was able to get most of his things (that he wanted) moved 5000 miles compliments of his employer. Of course, our house holds the rest. D still has tons of stuff in our house and no place to put it in her small room she’s renting 2500 miles from here.
Our carport holds things from H’s parents, who have been dead for over two decades. Yes, it would be good to get rid of but doesn’t look like it will happen anytime soon.
Sounds like many here have been good at disposing of “stuff.” Congrats!
We live in an apartment in Asia. My daughter’s room looks almost like it did when she graduated from high school 3 plus years ago, lol. Her room in our summer place in Maine is the same. We will have to deal with this at some point. Perhaps when we leave here (Asia) and all of our stuff gets merged after 20 years. That’ll be fun, NOT!
When I said upthread that we brought our sons their stuff, that was after they went through some of it and we went through the rest. I can be ruthless, but DH checked with them via text or photos before deciding what to keep. They each ended up with only 4-5 bankers boxes of stuff.
Shipping prices depend on what you put in the box. Sheet music and books can be shipped together inexpensively via USPS Media Mail. I would start there.
We have been downsizing our Christmas decorations each year for the last few years. Asking each family member to sort through their ornaments, choosing what to keep.
Also asking about general decorative items so that we don’t give away something super memorable.
It is possible to reduce your overall Christmas stash, and Pass along a few special ornaments to your children so they can store them and use them in their own homes.
Do you have a patio with space for a big outdoor bin? I bought a really nice HUGE one for around $100 at Costco about 3 years ago. I can get a lot of stuff in there. I’m talking A LOT. If you are ground floor, you can probably find one with a place for a lock. Some things like instruments couldn’t be in non climate control, but maybe you could shift some things around that can.
Your son is sharing an apartment. There very well might not be room for more extra “stuff”.
Both of my kids agree that the “stuff” needs to be small enough to easily be moved again and again.
I know you agreed to store stuff, but was that forever with you paying?
We will keep stuff while we own our house, but when we downsize, we won’t rent a storage unit for anything.
Maybe your son needs to re evaluate what he needs on the stuff.
@ProfessorMom1 - Well, that is a super idea about storage on the patio, but I cannot begin to tell you about all the RULES we have as to what is and is not acceptable to have on the patios! Ice chests are STRICTLY forbidden - not that you were suggesting using an ice chest, but I am pretty sure the type of bin you are suggesting would not be allowed. We can’t hang towels on our patios!
@thumper1 - yes, I agree. I am not sure he has room for more extra stuff. The instruments are what are the most challenging both storage and shipping-wise. Honestly, I can’t even remember what all he has in our storage unit. We probably need to go assess.
@powercropper - we could probably decrease the number of Christmas ornaments.
If the instruments are valuable one way to move them is to buy an extra seat on Southwest the next time you travel.
US Parcel Post or put it on the moving truck 
being that it isn’t a huge amount it could be worth it
Baby steps. Start by sending him the sheet music. USPS has the perfect size flat rate box that you can pick up and pack at your leisure. It is considered their “large” box and is a rectangle about 3 inches tall. I think the flat rate is about $17, but paper can be heavy so this might work for you.
Next I would tackle the Christmas decorations. They probably won’t weigh much, but packing them up to avoid breakage might be time consuming. Set a goal to get this done by mid November and send a box a week or all at once.
One day I started taking items out of my son’s closet and put things on the bed or floor in groups that would be easy to see on an iPhone screen. I texted him the pictures a few at a time. It took a couple weeks for him to look at all of them. He took the picture and saved to some app like instagram or snap chat where he put a red X through the items I should get rid of. You could do the same with the Christmas decs…
My parents handed off my sister’s accordion to her a couple of years after college. She did not store in a temperature controlled environment and I cannot recall which part has failed, but it would be very expensive to restore.
Thanks, @Kajon - I had thought of the sheet music in flat rate boxes as I had sent some to his university once. I know I can cull the Christmas ornaments. Some are definitely more special than others. That is a good idea to set a deadline. I can’t imagine shipping him Christmas ornaments at this point. As I have said before, if we have to continue to have storage for ourselves, I don’t mind storing his things.
And, yes, there is something within the accordion that is wax, I believe? I have heard that they must be stored in a climate controlled environment. His accordion was not expensive. Neither was the guitar he has. But, he did save his money for the accordion, and it was his first major purchase. The guitar was a gift from me. He is really a pianist. That’s what all the sheet music is.
He doesn’t have that much stuff - he has gone through all of it. We were with him when he did it, and he really has streamlined to a reasonable amount.
We likely do need to move to a different storage place. If we got one that is farther away from our home, I think it would be less expensive.
We have friends who live in the greater Atlanta area. Every single one of them has a storage unit away from their house…and a couple of them have been in your shoes…they wanted something smaller for the storage unit.
But where they are, these are common, and folks seem to rent them for what seems like…forever…and I don’t recall a change in cost every nine months (I’m sure the costs increase, but not that often).
Maybe you need to find a small long term storage place.
Re: that piano music…does he have a piano?
@thumper1 - yes, he has a digital piano. Took it to college with him, and has had it in CA ever since. We sold the grand piano when we downsized.
I don’t understand storage units if people have enough space in their homes - or they could have enough space in their homes with some effort. We just have to see if we can pare down to that level.
My mil had a friend who had a large storage unit filled to the brim with his mother’s things for nearly ten years! Never looked at it. Just kept paying and paying. Finally went through it all and got rid of it.