The loop has no town of its own, so you are choosing between a real service town, a lake village in the middle of the circle, a farm out among the greenhouses, or simply keeping your room in Reykjavik.
Selfoss — the practical base
The only proper town on the route: supermarkets, petrol, a hospital, a bus stop and rooms at every price. It sits on the ring road rather than on the loop, so you drive 50 to 60 kilometres north each morning, but it is the easiest place to restock and the obvious base if you are carrying on along the south coast afterwards.
Laugarvatn — in the middle of the circle
A lake village of a few hundred people, roughly halfway between Þingvellir and Geysir, with a geothermal pool, the Fontana baths and Efstidalur farm ten minutes up the road. You can be at Strokkur before the coaches. There are only a handful of guesthouses, so it sells out in July and August.
Reykholt and Flúðir — greenhouse country
Farm guesthouses and small hotels scattered through the horticultural belt south of Gullfoss, with Friðheimar at Reykholt and the Secret Lagoon at Flúðir. Quiet, dark at night, and you will need the car for absolutely everything including dinner.
Or keep the room in Reykjavik
The full circle is 230 to 250 kilometres and fits comfortably into a day, so plenty of people never sleep out here at all. That is the sane choice in December and January, when there are four hours of daylight and ice on the road, and it means your evening has somewhere to go. Expect to pay city prices for it.