First, yes you can rent costumes. The ones at the Visitor Center were pretty cheap, but if you want to price shop there are stores in Merchant Square that either sell or rent the kid's costumes, they also have a different selection.
Second, the taverns in the historical area are great, but they're not cheap. I recommend getting the most bang for your buck by going to the taverns in the evening after the Revolutionary City activities are done for the day. At that point all the taverns have re-enactors performing in them. Go earlier in the evening and they're more geared to families with children. Remember to ask for a tavern pin for your child before you leave, they give some nice ones out for no additional charge. Also, the portions are HUGE at the taverns, all except for Chownings, so keep that in mind when you order. I recommend splitting entrees, especially when you go to the King's Arms which is the best, but most expensive. You'll want to split the entrees there so you can try the soups and the appetizers. For breakfast and lunch, pack a meal and picnic in the gorgeous historic backyards, green before the governor's palace, the main green, the bridge over the canal, the gardens at the governor's palace, the pyramid overlooking the canal in the gardens, and so on. There's an awesome deli in Merchant's Square where you can get incredible (expensive, but incredible) cold cuts, fancy cheeses, breads, and so on for your picnic. You can also get cheaper meals and/or baked goods in the "garden" behind Chownings, the Raleigh bakery, or the newly opening coffeehouse. Cider and a ginger cake or sweet potato muffin makes for a great breakfast!
Kids may get antsy during the many "talking head" lectures (even if the talking head is wearing Colonial garb) and tours during the day, fortunately there are a few things that seem to really excite them endlessly: the gaol, capital, governor's palace, magazine, court, experts in the shops, silversmith, bookbinder, and printer. Then, in the afternoon to early evening there's a lot of action on Gloucester Street towards the Capital building for the Revolutionary City programming, all of which seems to be kid pleasing. Whatever you do, don't miss the Plantation, a newer addition, which is on the walk from the Visitor Center to the main Historic Area. In the Visitor Center, I think that the film about the Rockefellers funding CW dragged, and I'm an adult, whereas the film about the Patriot was all right and might be good for little ones.
On the way to Busch Gardens we stopped at the 
