There are pleanty of Holiday Inn express type hotels on US 1 less that 1 mile from the historic district that should be reasonable. I don't know what your price range is but there are sone nice B&B's that you may be able to find for $150 or so per night. (Maybe not while school is still out though)
St. Augustine is a great place to mill around. You'll have fun.
There are some reasonable places on US1. Close to the Honda shop. They get more expensive the closer you get to the beach and the Historical area. I have stayed at a Best Western at Hwy 16 and I95. Reasonably priced. Defineately check out Osteens for the best shrimp ever. It is east of the Lyons bridge. (about half mile).
Great Hotel off the beaten path.
La Fiesta Ocean Inn & Suites, St. Augustine beach.
We have stayed many times. Reasonable. They have a inclosed courtyard
parking area for the bikes. Which you can see from your room. Gives you
a sense of security at leaving the bike out at night. If you go by truck and trailer they have a special trailer parking area. Also Osteens is a must.
Great sea food at a great price. Enjoy Bob