We went with Keetsa, they are mostly online but have showrooms in several CA cities and NYC. They also claim to be an eco-friendly mattress if that matters to you. (It was mostly a nice little bonus for us, we weren't necessarily seeking a 'green' mattress. It isn't completely organic or anything, so you should be careful to read their claims and not get greenwashed.) I just hate the car-salesperson type feeling I get in mattress stores, so online was the way to go for us.
This was before tuft and needle (2012, I think) and casper (2014) were around, so they weren't options when we got our keetsa. But we are very happy with it. Basically it seemed like a good mattress at a good price, so we went for it. I also had a chance to check one out in person before we bought ours because my parents had gotten one.
Also, we always assumed we would upgrade from a full to a queen when we got a new mattress. But the more I thought about it, the less sense it made. For one thing, we were perfectly comfortable on the full, even with the occasional toddler and baby joining us. And what really killed the idea of the "upgrade" was a multitude of things: the loss of bedroom space, the need to get a different sized frame, potential new furniture purchase (or maybe less that we would need new bed furniture, but more that we really liked our antique sleigh bed), and new sheets/blankets to accommodate a bigger bed.
The prices for full sized beds at Keetsa (the Keetsa Plus that we got, which is the entry level model despite the 'plus' in its name) is $576. At Tuft and Needle a full is $500 and at Casper it is $800. Some may take issue with Keetsa's return policy (there's a 10% penalty), but if you are able to check one out in advance and like it, it's a good mattress at a decent price.
We ended up getting a nice metal platform foundation for our new mattress. We were using the old mattress' box spring for a while there, but wanted an upgrade. It was just a reasonably priced, well reviewed one from amazon.