The circumnavigation is roughly 1,500 to 1,700 kms. So that would be quite a chase to do that in 3 days, albeit rewarding. The circular route is tarmac, so basically doable in such a short time.
Travelling eastwards from Reykjavik takes you past the volcano and glacier of Hekla and further on to the Vatnajokull, which is the largest glacier in Europe.
Travelling northwards from Reykjavik will bring you to the remote north-western peninsula, which is just as rewarding.
If you are prepared to do sandy dirt roads I'd suggest to do the "Kjoelur route" which goes past the Gulfoss waterfall right through the centre of Iceland to Varmalidh in the north and then travel along the westcoast back to Reykjavik.
So, whichever way you go will be interesting
But be prepared for very strong winds, rain and low temps
And if you intend to stay in a tent, choose a place where the wind won't pester you too much...
Only when we pause to wonder
do we go beyond the limits of our little lives.