Perdón! donde puse "Cochabamba" quise decir "Copacabana". Se me confundieron los nombres de las ciudades...

Well first I would suggest staying in Puno for a night or two so you can visit some interesting sites in the area. Sillustani is a small pre Inca archeological site that is spectacularly located above a small lake on the other side of Puno from Titicaca itself,the ruins consist mainly of a few ceremonial funerary monuments known as "chullpas" .... though the site isn't anything major like some of the other ruins of Inca origin in the Sacred Valley I did find it a beautiful and somewhat enigmatic spot. Then there are some of the islands that should be visited on Lake Titicaca itself. First and most close to Puno are the Uros Islands,these are the famous floating islands which are home to the Uros people and a place that held a certain fascination for me since seeing them when I was a child on a documentary by French diver and explorer Jacques Cousteau. Yes they are a bit touristy but seeing these people making a home for themselves on floating islands built out of the native totora reeds is definitely a unique experience. There are guided tours to see them and they can be combined with my second recommendation for an island visit,that island would be Taquile,a pretty large island inhabited by traditional Andeans. The beautiful waters,blue skies and farmed terraces of Taquile Island reminded me of some sleepy Greek Island in some quiet corner of the Aegean Sea. As you wander around take note of the local men sitting around knitting,yes knitting for in their society it's the men who do the knitting while woman have other chores to tackle. Tours usually allow for a couple of hours to explore and the opportunity to enjoy a lunch which normally will include locally grown potatoes and fish. There's another less developed island called Amantani and I've heard of people spending a night or two with locals there so you might want to research that if you're interested. All in all the Uros/Taquile Island day tour was an excellent value and I felt the best way to round out a Lake Titicaca visit,I really enjoyed it! Now once you cross the border at Desaguadero you should head to the Bolivian lakeside town of Copacabana where there's a beautiful church dedicated to our Lady of Copacabana,mind you this is the original Copacabana,the famous Brazilian beach in Rio de Janeiro is named after here. In Copacabana I would suggest a visit to the church,here you'll see many fervent followers of the Virgin of Copacabana coming to pray and offering thanks for miracles granted,there's is much devotion to this Virgin in Bolivia. Another worthwhile activity is a climb up El Calvario to see the stations of the cross and take in the magnificent views of the town and Lake Titicaca. Word of warning do take the climb easy because the thin air at this altitude is no laughing matter,don't forget that Titicaca is considered the highest navigable lake in the world! There are two islands that can be reached by ferry from Copacabana that I'm sure are probably quite interesting but I have not personally visited them,these are the Island of the Sun and the Island of the Moon. Both islands contain several small Inca ruins and the Island of the Sun is believed by the Incas to be the birthplace of man. Visits can be arranged in Copacabana but do require time and a fair amount of hiking. Then from Copacabana to La Paz the other spot that should be on everyone's itinerary is the archeological site of Tiwanaku. This site is pre Inca and his considered one of South America's most enigmatic places,the ruins themselves aren't so impressive but the mystery behind them is and since it's on the way to La Paz I would not miss the opportunity to visit them. You can go online to search these individual sites I have mentioned or feel free to see my own reviews on Trip Advisor,any prior research will help not only with logistics but also give you a better understanding of the places and the native peoples that live here. Enjoy yourself and stay safe!

Bolivia/Peru Hop

Copacabana is a fun little town, rough and ready. We stayed three nights, which is plenty of time to get to see the islands. There are lots of tours and it is very easy to book. Another thing I would recommend is climbing Calvario - its a little hill that serves as a pilgrimage site. Lovely views of the lake on a clear day.

Hola hay buses que te llevan desde la terminal de La Paz Bolivia hacia la ciudad de Copacabana Bolivia, desde el puerto todas las mañana salen lanchas hacia la Isla del Sol y la Luna mas o menos demoras 1:30 hs en llegar. Las dos islas son hermosas con paisajes increíbles. Los boletos se compran allí mismo, salen por la mañana temprano y al mediodía. En mi caso contrate un tour de 2 días 1 noche, costo 90 dolares e incluía pasaje de bus desde La Paz a Coapacabana, almuerzo, city tour por copacabana, boletos de lancha para las 2 islas, recorrido por las islas, almuerzo en isla del sol y boleto Copacabana-Puno, guía turístico exclusivo durante todo el viaje y 1 noche de hotel en Copacabana, no me pareció caro y ellos te organizan toda la logística. Si venís del lado de Peru, hay micros que te llevan de Cusco a Puno, los boletos se compran en la terminal de Buses de Cusco. Otras opciones menos económicas y que demoran mas Tren algo así como 250 dolares, o Bus turístico con paradas. Yo realice uno salio 60 dolares hace varias paradas interesantes con almuerzo y demora mas o menos 10 horas con un guía y servicios dentro del cole. Si dispones de poco tiempo ninguna de estas 2 son buenas opciones. Una vez que llegas a la terminal de Puno, allí mismo te ofrecen los tour en lancha para recorrer las islas o sino también compras los boletos en el puerto. Yo los compre por la agencia de viajes del hotel donde pare en Puno (Casona Plaza), por internet desde Argentina, no me salio nada caro y lo pague en 12 cuotas con la tarjeta de crédito (Despegar). Los barcos salen temprano por la mañana y hace islas de los Uros (muy lindo e interesante) y luego 2.30 hs para llegar a Taquile, la vista increíble después de eso no tiene mucho mas y el viaje es largo regresas a Puno alrededor de las 6 PM. Espero te sirva mi experiencia. Mucha suerte!

I was on Peru Hop/Bolivia Hop, its a city to city, hop on-hop off bus. The boat tour by Peru Hop is an extra cost of USD 10, it's around 2 hours. I went from Cusco to Puno (7 hrs overnight bus). After the boat tour at Puno, moved on to Copacabana, Bolivia. From Puno to Copacabana is around 4-5 hours, including cross border time. Copacabana to La Paz is around 5 hours, at some point,you will have to get off bus and cross a river and the bus will cross the same river on another boat. If you speak Spanish and are adventurous, could take local bus, cheaper.. But they are crowded and would be a longer ride because of many stops.