Yes, Reykjavik is safe at night. The city has a low crime rate and is well-lit.
If you're looking for a party, then Reykjavik is the place to be. The city has a vibrant nightlife scene with plenty of bars and clubs to choose from. However, as with any city, it's always best to take precautions when travelling at night.
It's also a good idea to get travel insurance before you go to Iceland. This way, you'll be covered in case of any emergencies.