When I am downtown, the #1 place I would suggest is the Triple George Grill, which is on a side street across from the old Lady Luck. The place is set up like the Tadich Grill in San Francisco, and the food is fantastic. I highly recommend the cioppino or the stuffed shrimp. The steaks and chops are also very good.
Hugo's Cellar is another place that has excellent food, but is a little more pricey than the Triple George. If you are looking for a romantic evening, then Hugo's might be the way to go, but make sure you get a reservation. If you are going with a group of 4-8 people, Triple George has nice private booths (many of them) for just such an occasion.
Finally, the Binion's Ranch Steakhouse offers both great views and steaks (located on the top floor of the building). The prime rib cuts are huge. They say the cut I got was 18 oz, but it was easily double the size of the 16 oz. steak my friend got. The place definitely has an old Vegas appeal.
I'd second the recommendation for Binion's Steakhouse. The food is very good there (I'd recommend the strip steak with the blue cheese, quite tasty) and it is a nice view of the town from the restaurant. Many locals I've talked to say the steak is comparable to good steaks on the strip, but less expensive. Also, it does have a great old Vegas vibe. While I've not eaten at Hugo's Cellar, I've always heard very good things about it.