Hotels will always be pricier in March due to Nowruz (Iranian New Year), but now because of the sanctions, all hotels are very very cheap. A couple of years ago (my first time in Iran) it was 10.000 to the dollar. Now it's 30.000 to the dollar so things are generally 2-3x cheaper depending on what it is. Hotels are cheaper, however, imported goods are the same price (in dollars) as they were before.
CouchSurfing is a great tool for finding interesting places to stay and so many Iranians are incredibly quick to accept requests.
The best place for interesting hotels (that I found) was in Yazd. So many boutique places in traditional courtyards for around $20-$30. Really really nice places to stay - bear in mind though that you'll need to be married if you wish to share a room with the opposite sex.
Tehran has a lot of options, the cheaper end of the scale being Hotel Firouzeh and Hotel Khayyam as already mentioned. Now they're around $10 a night. Both basic but do the job.