If you are thinking of visiting Lake Titicaca, you have to be in Puno. Puno itself is a pretty tourist city. You can reach Puno from Cusco. I think the best way to reach Puno from Cusco is by train. To me this journey was unforgettable. I believe this is one of the best train journey you would ever have. This journey passes through the Andean mountains and valleys of the Huatanay River, before reaching the Andean Plains, La Raya (the highest point of the route) and finally Cuzco. You can reach Puno by bus too. You can reach Puno in 8 hours from Cusco.
What to see in Puno..
Certainly you go to Puno to see mainly Lake Titicaca, Reed island or Uros. But Puno is nice city too. You can visit some places of this city while you are staying here. You can visit Church of San Pedro or the Sistine Chapel of the Americas.
There are a good number of hotels you may find in Puno. One of the expensive one is Libertador Hotel. But this one is not in the city. Once you reach the city you have to take a taxi to go back to this hotel. There is another option, train passes by this hotel and there is is stoppage there. You can utilize the stoppage.
There are other hotels which are just in the center of the city. These hotels are in the range of 30 to 40 dollars. Some of the hotels are Hotel Colon Inn, Hotel Casa Andina Plaza, Hotel Casona Plaza.