I lived near Irving and Ashland- there was a tacqueria on that corner that offered a "deluxe" burrito, steak or chicken with your choice of fillings (lettuce, onion, tomato, sour cream, cheese) for $4.95. There was a place further down Irving (near Sheridan) that was awesome too but their burrito was $5.50 (It was a sit-down place).
Tucked under the El track on Sheridan is the real gem- they have a gyro spit loaded with sliced pork, spicy sauce and pineapple that they slice off crispy hunks of to make your "Burrito al pastor" Man, those were transcendental.
If you're up for a walk, There is a full-service place on Montrose & Paulina that makes an awesome burrito- but I almost always get the guacamole tostado. I hear that my favorite 24-hour tacqueria, up on Lawrence and Paulina just closed

. They used to make awesome enchiladas for $5. When I lived on Paulina north of Montrose, it was great to get off the bus there after a night out and get a $4.50 burrito. Mmmmmm! Breakfast of champions!