Lake Titicaca - day tour or stay the night

I have been thinking of skipping Puno and Lake Titicaca and go straight from Cusco to Arequipa, but on the other hand I think that I shouldn't miss Lake Titicaca when I am in that part of the world.

One option is to spend two nights in Puno and from there take an organised day tour to the islands.

Another option is to spend one night in Puno, one night on Taquile or Amantani and then one more night in Puno before going on to Arequipa.

It leans toward the last option. What's your option? Is it worth staying a night on one of the islands instead of taking a day tour?
Which island, Taquile or Amantani, would you recommend and why?

Personally, I didn't think much of Puno so didn't stay there other than to go out to the floating islands (very touristy but worth doing). It should be possible to arrive in Puno in the morning, see the floating islands and then leave for Arequipa in the late afternoon. Arequipa and Colca Canyon are fabulous and certainly worth the time at the expense of Puno.

If you can get out to the Isla del Sol from Puno, that's worth a trip but I think it's more accessible from the Bolivian side at Copacabana.

Other than the islands on Lake Titicaca, the sites around Puno are hardly big ticket attractions. None are within the town itself. I did take a short day tour out to some archeological tombs. They were of mild interest. Puno actually does not have that many hotels and I had difficulty getting a room because of all of the large bus tours going through.

Thank you for the answers! Staying in Puno is not on my wishlist, but as I don't travel with night buses I guess I need to stay one night in the city before going to the islands and one night after, depending on when the boat returns to Puno. For example, it says in my guidebook that ferries leave Amantani at 4pm, but sometimes at 8am. If arriving back to Puno early, the best option seems to be to take a bus straight to Arequipa.

I was there just last year, and Puno is definitely not worth the stay...If you are heading to Bolivia, I recommend stopping in Copacabana and doing the lake tours from that side. Copacabana is much more relaxed, even if you don't want to do any tours you can enjoy the lake much more from that side. The lake from Puno doesn't look the most attractive, it's full of tour touts whereas from Copacabana the lake is so much more appealing.

I did this trip in July, and the same evening I arrived in Puno I booked a 2-day tour starting the next morning. The tour took us to the floating islands and then to Amantani. I liked Amantani very much and stayed in a lovely family. The next day the boat took us to Taquile for a walk and lunch, before returning to Puno.

Unfortunately there was no time to visit Bolivia during this trip. That will be another year

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