Hi Katya
We were in Mozambique in 2001, so things may have changed, but I would recommend the following places (I hope that they are all still there as we are planning another trip):
In Maputo there is "The Base", a very clean, friendly Backpackers Lodge, with shared dorms for about 6 people or they do have a couple of twin rooms, but no camping.
Near Inhambane on the coast is Tofo, we camped at Bamboozi Backpackers, just in the dunes by the beach - gorgeous. Very simple place with a beach front bar that serves lovely food, and we paid about 60,000 meticais per night (for two people).
Lastly in Vilankulo we camped in a beautiful spot at Vilankulo Baobab Beach, it also has little huts in the trees.
I hope all of these places still exist, we found when we went that some places had just changed names a few times, so they might be there but called something else. It is the sort of country that you can travel in and just arrange accomodation as you go, we never had to book ahead, all the locals and other travellers always tell you where there are rooms or camping. Have a lovely trip!
Regards, Chantal