The Snaefellsjökull is a glacier located at the extremity of Snaefellsnes Peninsula, but when the weather is clear it is also visible from Reykjavik!
The first time I visited the peninsula in September, I literally did not see the Snaefellsjökull! Thick fog prevented us from admiring its slender shape and characteristic little peak at the summit.
I have made up for it since then and have been able to admire it from all angles. A track allows you to approach the glacier but it is reserved for 4x4s and my little Suzuki Swift couldn't have taken me there. Maybe some other time, I hope.
Even though I have done good deal of hiking on the peninsula, mainly along the coast, I still haven't managed to do the 5-hour climb to the glacier Maybe you'll be luckier! In any case, give yourself at least a day to visit the surroundings, the ideal being to spend at least 2 days in the national park.