Problem is, you are about as far from the core of downtown Fort Worth as you can be while still being located downtown. As others have said, the downtown dining and nightlife is 8-10 blocks north of the Sheraton & convention center.

I know there are a few small convenience stores downtown, and in perusing google maps there may be one a block or 2 north of the Sheraton. I think there may also be one around Houston & 6th, which will be on the other side of the convention center and 6ish blocks north of you.

I've been to the T&P Tavern once. It was OK, I just never really think of it when going out.