In May this year we flew into Chania and stayed for two nights in the small village of Panormo, not far along the coast east from Rethimno, about a mile from the main coastal highway, so very quiet with a harbour, a couple of beaches and some nice restaurants and in a good position for visits to the south , east and western areas of the island. We then drove to the very far east basing ourselves near the town of Sitia, an almost totally unspoilt area of the island. Not a lot of facilities but some great restaurants and beaches.
I think most places that have a nice beach will be somewhat touristy. I have only visited Plakias on a day out and it seemed attractive with a good beach. Many of the resorts on the north coast are quite large and are very touristy. Rethimno is a working town as well as a tourist resort, nice beach and a long sea front area to the many hotels and apartments and may suit your needs. Almyrida near Chania (also well worth a visit) a small holiday resort is quite nice, nice beaches and restaurants . We have stayed there in an apartment, sadly without a sea view, and there is no main road running through the resort. Nearby Kalives is even less of a tourist centre, more of a working village with beaches. We also visited Stavros which is just a few miles from Chania, the very small resort didn't seem touristy at all there was a beautiful beach and a lagoon as well as the sea, though I suspect it may be extremely quiet.