I am on vacation from school in the last half of March thru first half of April. This is the last real vacation time I will have for a while and I wanted to go on a trip with my parents for a week or so. But, my dad can't handle walking very long distances due to his arthritis. We live in Florida so no reason to visit there.
I was thinking maybe California but not sure what the weather would be like. Any suggestions would be greatly appreciated!

It is a big state so I am sure the weather will vary. You can check historical average of towns or cities you are thinking of visiting on any of a number of weather related websites. SF is nice but won't be good in my opinion given your walking restraints.

You could do a trip into San Francisco, drive down the coast and stop for the wonderful views, then drive back north through wine country or over to Yosemite (only the valley would be open, but much can be seen from a vehicle

It will still be too cold for New England. Washington after Cherry Blossom is nice if they haven't been there too often.

I would look for good flights to the Bay Area and go up to Napa, Sonoma, and Mendocino. The scenery is beautiful and the towns are interesting even if you never drink a drop of wine. You can do as much or as little walking as you like. It could not be more different than Florida, if you want something different.

You can then drive down through the wildly beautiful Point Reyes area and spend a few days in San Francisco. A ferry to Tiburon or (more crowded) Sausalito is a great way to spend a day, and again, it does not require a ton of walking.

Early spring in these areas is gorgeous, especially around the Bay itself.

Those are really helpful suggestions! Thank you!