Accommodations can generally be had quite cheaply throughout Nicaragua. Options range from simple hammocks ($2-$3), to dorm rooms in hostels ($5-9), to private double-bed ("matrimonial") rooms ($10-35, depending on presence of TV, A/C, and private bathroom). You will find more expensive hotel accommodations in some cities as well.
While Barrio Martha Quezada has typically been a budget destination for visitors to Managua due to its many inexpensive hotel options, it has become increasingly dangerous, especially for tourists, with robberies occurring in broad daylight. Unless you need to be in this area to catch an early morning bus from a nearby terminal, it is advisable to avoid Martha Quezada, particularly since it is far from what is termed the "new" center of Managua. The area near the Tica Bus station has a reputation for being dangerous as well, and tourists may be well advised to take a cab directly to and from the station, even if the walk is short. Backpackers Inn near MetroCentro (5min by taxi from the UCA microbuses), Hotel San Luis in Colonia Centroamerica (5 min by taxi from Mercado Huembes bus terminal) are good budget options in safe neighborhoods, as are numerous hotels of various prices in neighborhoods around the new center near Metrocentro and Caraterra Masaya (i.e. Altamira, Los Robles, Reparto San Juan).
The Managua Backpackers inn is a great place to stay while in Managua. It is very clean and it is in a quiet neighborhood. The owners are amazing and if you're lucky, you might have a beer with one of them at night. There is a pool and free Internet access and wi-fi on location. A kitchen is also available for use. Ticuantepe is quickly becoming the place to stay because of its safety. There are a couple of lower-priced hotels, including Viva Guesthouse and Aires del Tiempo. They are both priced around $30 and have wireless internet. Viva Guesthouse does have a pool.
Look for pensiones or huespedes or hospedajes as these are the cheapest sleeps costing under US$5. They are usually family owned and you'll be hanging out with mostly locals. Make sure you know when they lock their doors if you are going out at night. Hotels have more amenities but are more expensive. There are some backpacker hostels in Granada, San Juan del Sur, Isla Ometepe, Masaya, Managua, and Leon otherwise it's pensiones all the way.