We went on a trail ride with Laxness horse farm, located only a short drive from Reykjavik, which also arranges transportation. This is a family run operation, and they clearly love their horses and love the people who come to hang out with them. I highly recommend this company!
Earlier in the day we went caving in Laederandi, a lava flow cave just outside Reykjavik. It was about a two hour trip, with excellent guides.