Your tour will most likely stop at Reynisfjara and puffins are there. If you want to see them separately from that, I would take time away from Reykjavik and rent a car for one night and head to Westmann Islands. The south tip of the island is where the puffin lookout is. The puffins are on land there in the early mornings and later at night, so an overnight works best for this.
You could also either rent a car or take a tour and do Snaefellsness. You could stay a night up there, which I would recommend. I would rent a car vs a tour, but either will work. If you like soaking, then hit Hvammsvik on the way up or back. This is my favorite commercial hot spring in all of our trips, FWIW. The cold plunge is the fjord, and the scenery is stunning and the hot pools are so relaxing.
I have not been to Perlan, but my husband did when he had time to kill on his trip this past summer. He said it was fine, but mostly because it was new to him and gave him something different to do. There is so much to do right in Reykjavik that you could easily skip this and see more with the time. Here are things that we enjoy right in the city:
Walk from Sun Voyager to Harpa, and check that out inside as well.
Food tour
Citywalk "Free" walking tour (tip at the end)
Walk up Pufa
Visit the Handknitting Association store on the Rainbow Road.
Visit Hallgrimskirkja, which is the big church, and get tickets to go up to the top for sweeping views of the city.
Phallological Museum (yes sounds silly but is rather interesting)
Just wander and check out all the street art. There are huge murals all over, so be sure to get off Laugarvegar onto the side streets, even blocks away to see some of the best.
Get a hot dog, they are so good! Any hot dog stand will suffice, you don't have to go to the most famous one.
Go to a local pool in town. I like Sundhollin, but there are others. Sundhollin has rooftop hot tubs though, so that is really nice!
Go t o Sky Lagoon, which is in Reykjavik, but about a 10 minute drive/taxi/bus ride away.
