As long as you are going to be in Hammond, I recommend eating at Trey Yuen. It is a good (and VERY large) Chinese restaurant there that specializes in preparations of locally caught seafood -- they do that better than they do the more traditional things. Their crawfish in lobster sauce is yummy. (You will get plenty of excellent traditional and perhaps not-so-traditional Louisiana cuisine while you are in New Orleans, but Louisiana Chinese food is kind of a unique fusion that is worth trying if you get a chance.)
From Hammond you are looking at a drive of about 3 hours to the Dome in game traffic. If the hotel is offering a bus, you might wish to take it. (The drive from Hammond down to the I-10 interchange is normally about 30 minutes, but it will take longer on game day. From there you will turn east on I-10 and cross the Bonnet Carré spillway. Once over the spillway, the traffic will become more dense, and by the time you reach the I-10/I-610 split near the Orleans/Jefferson parish line it will have slowed to a near-standstill, and it will be that way all the way to the exits for the Dome.
BTW, if you do drive in, here is my preference for the Dome (and other major events near Canal St.) when coming from I-10 West: I switch from I-10 to US90 as I come into downtown, and exit US90 at Loyola, turning left under the highway. Off Loyola, I turn right onto Girod, which leads down to the area near the courthouses. The parking lots and garages of the major office buildings in the CBD are normally open for special events, and parking south of Poydras in this area puts you in a good position to get back out of the city westbound. The going rate for a flat-rate advance-reserved parking space for the game in the CBD garages ranges from a low of about $30 to a high of nearly $350; the closer to the Dome you are, the more it costs. I would recommend parking in the warehouse district relatively near the river and grabbing the #16 bus up Poydras to the Dome.