In the budget range is one of the best values you’ll find anywhere in Guatemala. Casa D’Acuña (4a Calle 3-11 Zona 2, tel. 7951-0482 or 7951-0484, casadeacuna [at] yahoo [dot] com) lies at the bottom of a steep hill south of the main plaza and has four comfortable dormitories with four beds apiece ($7 per person) as well as two private double rooms ($13 d). All rooms have shared bath. There is also an excellent restaurant built around the main courtyard of the colonial building in which the lodge is housed.
On the next street over toward the park is Posada de Don Pedro (3a Calle 3-12 Zona 2, tel. 7951-0562), with acceptably comfortable beds and five rooms with shared bath at $5.50 per person along with two rooms with private bath for $8 per person. The main entrance doubles as a small corner store.
Though not a budget accommodation per se, 
Hostal de Doña Victoria (3a Calle 2-38 Zona 3, tel. 7951-4213/14) has a shared-bath, bunk-bed dormitory where you can stay for $3.50 per person.
North of the main plaza and conveniently situated near the bus terminals (though not in the best part of town) is Posada Don Juan Matalbatz (3a Calle 1-46 Zona 1, tel. 7951-0811). It has rooms around a pretty courtyard in a neocolonial building with somewhat saggy beds, cable TV, reading lamps, and ancient hot-water heaters. There are rooms with shared bath for $8 per person and some with private bath going for $26 d. There’s also a café downstairs with a pool table.
It doesn’t get any cheaper or more basic than Chipi Chipi Hostel (1a Calle 3-25 Zona 1, tel. 5226-0235), just off the main plaza, where a bed in a shared-bath dormitory can be had for $3.50. It has an Internet lounge and hammock area.
A few blocks west of the plaza is Pensión Monja Blanca (2a Calle 6-30 Zona 2, tel. 7952-1712), run by a charming elderly couple who keep the place spotless. Centered round a lovely garden are comfortable tiled-floor rooms with shared bath ($7 per person) or private bath ($26 d). There are a balcony with a sitting area, a pay phone, and a pleasant tea room where you can have breakfast.
Friendly Hotel La Paz (6a Avenida 2-19 Zona 1, tel. 7952-1358) is another good budget option with basic but clean, cheerful rooms with electric hot-water heater for $10 d.
Hotel Cobán Imperial (6a Avenida 1-12 Zona 1, tel. 7952-1131) is an old standby popular with Guatemalan families and has rooms with TV and shared bath for $8 d or rooms with private bath with electric hot-water heater for $17 d.