cocktails/appetizers downtown Tampa
Malio's Prime is just south of Curtis Hixon park, about a block south of the theater's parking garage on Ashley Street. They overlook the river.
On the flip side of that coin, if you don't mind hanging with the local punks and drunks, you could always go for some of the highest octane "cocktails" in Tampa at The Hub, just a few blocks east of the theater on Franklin Street... :)
I suggest Fly, which has great cocktails and small plates, and outdoor (as well as indoor!) seating. It's not along the river, though, it's about 2-3 blocks from the Straz on Franklin.
If you really want to sit by the river, the Straz serves dinner and drinks both indoors and on its terrace.