My parents are tour guides in SA, so I called them to ask your question. Not a great answer, as there are TONS of hotels here, and these three places you're going are not really close to eachother.
Dad suggested the Motel 6 on I-10 just outside loop 1604 (cheap).
He also said that the Drury Inn on the corner of I-10 & 1604 (just inside the loop) is nicer. He said that these two hotels are about 10 minutes to Seaworld, 15-20 minutes to the Riverwalk, and you can see Fiesta Texas from these hotels.
He said that sometimes Hotels.com can give you a deal, but suggested that you call hotel management to try to broker a deal too. Spring break will be full, so sometimes trying both ways to get a room will be your best bet.
Good luck. There are always places downtown by the Riverwalk, but during spring break that might be noisy & pricey. No cheap grocery store or cheap shopping nearby. If you get a place off of I-10 & 1604 area, you'll be close also to an HEB, eating, Target, etc. There's not much by Seaworld, last time I went there 10 years ago. Of course, I'm sure that's changed, but a place by Seaworld, in my opinion, will be far from Fiesta & far from Downtown.
Don't forget to go to the Alamo if there's time (downtown). The Buckhorn Museum is a great place to go for lunch (downtown). There, you have to pay to go into the museum, but if you just go for lunch you can still see a lot of the deer and taxidermied animals on the wall. I hear that the Ripleys Museum is neat too, but I've never been (also downtown). The Pearl Brewery has free tours Saturday mornings, if that sounds like fun. I think they're at 10am & 12noon. Never been, again, but my mom does the tour every Sat morning. At the Pearl, there's a local farmers market, selling fresh veggies/fruits, plus homemade jams, soaps, jarred olives, etc. The Pearl is near 281 & Josephine.
Have fun!