If you want to treat yourself for a little more money (but without breaking the bank), go to the Triple George Grill opposite the Lady Luck. They have an excellent lunch menu with $10 meals. Otherwise, deals are plentiful anywhere on Fremont...just about every casino has coffee shops, snack bars, or eat-in restaurants. Another of my favorites is the 777 brewpub in Main Street Station.
Don't forget the Binion's burger, and in the evenings, Binion's Bullpen has for $4.95 a 20oz beer, bag of chips, and a hot dog (which you load up with items from the condiment bar such as bacon, olives, peppers, feta cheese, etc).
If you're in a small group, Chicago Brewing Company in the Four Queens has excellent pizzas. Several places have full prime rib dinners for $8 or so.
Splurge a bit if you get a chance and try "Top of Binion's" steakhouse one night....they have nightly specials for $20 , with great views of Vegas in an old-style-Vegas steakhouse. My wife ordered the special last time, which was a NY strip with crab legs. Great deal!
You're going to be downtown....there's still great deals everywhere. Not so much on the strip.
(Edited to add - the places I listed above are not the cheapest on Fremont - there's cheaper - but these are among the best IMO.)