For cheap and cheerful I like Guzman Y Gomez. They are all over Sydney, and offer seriously tasty Mexican food. Most of their menu is gluten free, which is a huge plus, and they offer dine-in or takeaway so you can suit your moods.
The Dip @ Goodgod Small Club on Liverpool Street serves up nice burgers and hotdogs although it's more of a mix of American-Mexican food. I would recommend trying the Braised Beef Short Rib Nachos and Hot Wings! Yumm
Barrio Chino (Spanish for Chinatown) Tasty and authentic Mexican food (no sour cream or tasty cheese in site.) Knowledgeable and cheeky staff, cool crowds but not too cool. Awesome drinks list and good vibes coming from the DJ. Highly recommend.
Dos Senoritas in Gladesville. It is small and has a real shabby chic vibe to it but the food is authentic and delicious. The chef is actually Mexican and while you're there you actually feel like you're in a taqueria in Mexico. Really well priced too.