Tommy Bahama - Never tried it, but I'm skeptical. Seems to be priced a bit high, probably because of the name behind it and the extensive advertising campaign. I saw it prominently displayed on every liquor store shelf within days of the release (it's new this year). From what I've read, it's a decent rum, not bad, but not good either, although overpriced for what you get.
I agree with the Rhum Agricole recommendations. Of those, the Neisson is the only one I've got, and I have two others picked up from the Caribbean, Trois Rivieres and something else I can't remember this early in the morning. This style of rum is different from all the others. Some of them remind me of single malt scotch, though I'm not a Scotch drinker, and my Dad (who is) thinks I'm crazy.
Never had Zaya, but Zacapa Centenarios is good. Very smooth, fairly sweet as well. If you like sweet, try Pyrat XO or Pyrat Pistol. They're on the sweeter side, with a bit of an orange flavor as well. Not quite a flavored rum, but not really a 'regular' rum either.
The Pampero Aniversario is one of my favorites. It has a lot of flavors from the oak aging, similar to an oaked Chardonnay. If you like that style, try Ron del Barillito 3-Star from Puerto Rico if you can find it. The Santa Teresa is good also, but the oak flavors aren't quite as prominent, the rum stands out a bit more.
If you don't have a good liquor store nearby, look for Cruzan Single Barrel or Mount Gay Extra Old. Both are readily available, and are probably the best thing you'll find in the typical street corner liquor store.
You may also want to try a bottle of Gosling's Black Seal rum. It's well known as one of the best black rums on the market. Cruzan Blackstrap is similar, but most people complain of a heavy molasses flavor. Gosling's is not as heavy as the color would imply. Their gold rum is decent too, and I've heard great things about their Family Reserve but I haven't tried it yet.
The Angostura line of rums are also good, though 1824 will set you back considerably more than the 1919, but there is definitely a distinct difference between the two. The 1824, being aged longer, has more of the toasted oak flavors that I enjoy, and has a bit more body to it. If you find one at a good price, it's worth it, but in this range it's worth shopping around the price.
You can probably tell by now there can be huge differences from one rum to the next. Look around for a local rum bar and try a few different brands side-by-side, you'll probably be surprised how different they taste. Rums from different countries can vary as much or more than Scotch from different regions. The best part is they're a helluva lot cheaper.