Q: Where can I rent a little boat in Reykjavik? I would like to have a little trip (some hours) around the city’s coast.
A: There is no boat rental in Reykjavík and your supposed little trip on open sea is not for everyone.
You have two choices: take a whale watching and puffin tour from the old harbor, or stop a small fishing boat coming into the harbor and rent it with the captain. I have not tried it but it could be a different experience.
On the other hand, there is a walking path along most of Reykjavík’s coastline. That is one alternative to see the coast, on foot.