Hot Pot other than Blue Lagoon

Mývatn Nature Baths in the north are the real deal. There are also "wild" hot pots here and there. We came across a few in Hoffell Hot Tubs. 

I like Sundhöll Reykjavíkur thermal pool in  barronstigur central Reykjavik next to the hallsgrimmkirka.  Lovely art deco building with ht tubs on the rood open late.  I understand your fears about driving.  I will hire a car for the first time this February but only if its a 4 by4. I have had great tours in small minibuses with gateway to Iceland's great guides. They do a hot golden circle tour which includes waterfalls geysers and the 'secret lagoon'.  They will do private tours and you can go further south to the glacier lakes. With a driver you at least get to enjoy the the very special scenery.

All tours will pick you up from Reykjavik. Waling around lake tjorn in the winter half light gives you great pictures. Recommend iheart Reykjavik waling tour particularly if you like street art.

Have a lovely time. 

Iceland has an excellent road system, minimal traffic outside Reykjavik, road signs are in both English and Icelandic, and mobile phone coverage is good even in desolate areas.  In other words, it's an easy country to drive in, so why spend the extra money on a private driver when you can rent an economy car with GPS?

The Blue Lagoon is a must, and since it's so close to Keflavík International Airport it makes a convenient first or last stop in any visit to Iceland.  Other hot spot recommendations are Þingvellir, Gullfoss Falls, Geysir and Bjarnarhöfn Shark Museum, all of which are 3 hours or less from Reykjavik.  

If you do rent a car, rent it from the facility next to the BSI Coach Terminal in Reykjavik (Hertz, Budget and several local companies) rather than at Keflavik airport.  Rates are much lower, and you can take the Flybus shuttle between the airport and the BSI terminal.