If you only have a day free to travel outside of Reykjavík, there are a few places you could visit. Snæfellsnes peninsula is one of Iceland most spectacular places and includes most of everything Iceland has to offer in one place. The peninsula is one of the best places in Iceland to see basalt columns.
Gerðuberg basalt columns
At Gerðuberg, you can see an impressive row of columnar basalt which is between 7 and 14 meters high.
About a 30-minute drive away is Ytri-Tunga, a known seal colony. The best time to see them is during the summer, but they reside there all year around.
The 80 meters high Bjarnarfoss is a great sight to see. It falls down a basalt cliff which was formed by the now extinct volcano Mælifell. Then, the waterfall drops into the Búðarhraun lava field.
The nearby village Arnarstapi is a great place to go bird watching, and it has, for example, a significant arctic tern colony. Walking along the coast gives excellent views of Snæfellsjökull glacier, the columnar basalt coast, and grottoes.
If you continue west from Arnarstapi, you will come to Djúpalónssandur beach. The beach was once the home to some 60 fishing boats and prolific fishing villages in Snæfellsnes, but today the beach is vacant. On the beach, you see lifting stones, which were used to test the strength of fishermen. Their names are Fullsterkur (full strength), Hálfsterkur (half strength), Hálfdrættingur (weakling) and Amlóði (useless).
Small villages on the Snæfellsnes Peninsula
Other places to visit on Snæfellsnes is the villages Stykkishólmur and Grundarfjörður, the famous Kirkjufell mountain, and Berserkjahraun lava field. You could also go on a snowmobile ride up Snæfellsjökull glacier or hike it and visit Vatnshellir cave.
Then, if you stay past sunset, you might be able to catch the Northern Lights over the glacier or Kirkjufell mountain.