Find free camping at shady River Park at the end of Main Street, but it has no running water. Also on the river, but a bit farther from town, is Talkeetna Alaska RV (907/733-2604), with in-the-trees tent and RV sites for $20. There are no hookups, but showers ($2) are available. Talkeetna Camper Park (907/733-2693, www.talkeetnacamper.com [1], Apr.–Oct., RVs $36) has wooded RV sites; it’s on the right just before you enter town.
Take showers and wash your clothes at Washi-Washi on the south end of town, or at Suds, the coin laundry behind Twister Creek Restaurant.
Links:
[1] http://www.talkeetnacamper.com