You can choose from several options!
Some of the private campgrounds are extremely reasonable when you're renting for the whole season - as in around $300.00 a month, some include utilities, some don't.
BLM (Bureau of Land Management) has several LTVA's (Long Term Visitors Areas). None have full hookups, some don't even have pit toilets. Depending on what you're driving/living in, which of the LTVA's you'll be able to stay in. Cost is $180.00 for the whole winter season.
BLM and National Forest lands have dispersed camping. No facilities whatsoever, no charge however. You haul your water from town, take your own garbage out and dispose of your own toilet contents. The most important rule is that you must move every 14 days.
There is also free camping on National Wildlife Refuges but it's generally limited to 14 days per year, per refuge.
Somewhat close to town is a very subjective term. I consider somewhat to be within 45 minutes to an hour of a W/M, others think that anything more than a 10 minute drive is excessive.
Lots to choose from! Finding low cost places to stay is the least of the concerns for a newbie. Making the decision of what and where is the harder part.