If it's old you want, St. Augustine is your best bet, but it's more than an hour from Orlando; it's about 125 miles north from WDW. St. Augustine is the oldest continuously occupied city in the United States.
http://www.ci.st-augustine.fl.us/visitors/specialplace.html
Most of the other colonial-era sites are down in the Keys, but most things that date back to before Flagler are counted as old in Florida. There are some interesting places that date to the early 20th century that are worth a visit.
Closer in, if beach isn't necessary, you could try Mt. Dora, which is ~1 hr. north of Orlando; these days it's kind of considered an outer suburb. Mt. Dora has a very nice old central business district, and there is a thriving antiques trade there.
http://ci.mount-dora.fl.us/services/general.htm
Even closer, as in *in* Orlando proper, there is Winter Park; the original good neighborhood in Orlando, a couple of miles north of downtown. There are a lot of nice homes to look at, a little river cruise in summertime, some toney shops and galleries, Rollins College, and a few museums, among them the Morse Museum, which has the largest collection of American stained glass in the US. If you like Tiffany, this is the place.
http://www.wpfl.org/
Closest of all, the Osceola Pioneer center is a tiny little museum off of 192, on Bass Rd., that focuses on the cattle-ranching heritage that is important in Osceola County (ranching was the primary employer there pre-Mouse and still happens in the parts of the county farthest away from WDW.)
http://www.evilla-rentals.com/pioneer-center.htm
BTW, a spelling note if you are looking it up; the Cuban area in Tampa is Ybor City.
