Here are parties that we've had that have been a success.
Pump it Up
Rolly Pollies (kids LOVED this one - it is on Hillsborough Rd)
Little Gym (back in TX, but I'm guessing the one here would be the same)
La Fleurs Gym (or any gymnastics place)- great for 3 yr olds w/lots of energy!
QZAR, Bowling & Skating (too little for these now, but that day will come!)
We did Old McMickeys farm, but it is gone now. I think up in LOL there is Grandmas something or other that is similar.
We went to a party at the zoo but it was geared towards older kids - they might have a more 3yr old friendly program. Same thing with the MOSI party - they did crafts and such that were for kindergarten / 1st grade (age of the party boy), but I'd think they could adapt to age of child.
If you want to supply all the fun, you can reserve the covered areas at parks... no clue how, but I've seen lots of parties at Lake Park and the one over in Oldsmar (Phillipi Creek or something like that)