Two nights doesn't give that much time, just one clear day.
A lot of flights seemed to arrive about 9 am so you could do Sky Lagoon or Blue Lagoon and Reykjavik on arrival day.
The full day could then be spent on the Golden Circle or further afield if you don't mind a very long day.
The ring road is fine in the summer but there are lots of warnings about the dangers of winter driving.
With such little time I'd go on a minibus tour. They know where they are going and are used to the driving conditions in winter. (I had originally booked for April and was surprised that that was still winter).
We self drove but it was summer and we had a week, so no more than 4 hours driving most days.
We used Troll Expeditions for a couple of activities and they were great - and a little bit cheaper than some others.
They do Golden Circle tours but also add on going on to Vik via Seljalandsfoss and Skógafoss waterfalls or even to Jökulsárlón if you don't mind a very long day.
The plus point is that they explain what you are looking at, the history and geology, which you don't get on self drive.