Flying in Iceland while on holiday

[METARHIMS]

I'll be in Iceland in October and I'd like to do some flying while I'm there, if possible. I'm writing to ask for recommendations. I'm a professional pilot in the U.S.

Obviously, I'll be flying into BIKF but I'll spend most of my days in Reykjavik, Akureyri and points in between.

I was thinking I could either take a domestic roundtrip flight out of BIRK for a day trip and see Iceland from the air or rent a G.A. airplane with an Icelandic instructor. Which do you recommend?

Thanks,

METARHIMS