Europe 10 day itinerary

You could do the classic Venice-Florence-Rome trip easily in 10 days. Swimming in Venice at Lido beach, and in Rome at Ostia, easy train ride from Rome. Don't know about water temperature that time of year. Hardly think any of these will bore you. Venice has a special 3-day transport pass for people under 25 or so called the Rolling Venice Card.
Fly into Venice and home from Rome, to avoid the ubiquitous early morning departures from Venice airport.

The water in the Mediterranean sea is never hot, at least to me. It is not like the Caribbean, Thailand or Florida. And in June, the water is even colder than September. But I love to swim in the Mediterranean sea: the water is crystal clear, and various shades of blue are amazing. Plus often I can do spectacular hike along the ridge and jump in the water at different points.

It seems like you need a very fast paced itinerary to hold your attention. I think that you would do well in Greece or Italy or Spain.

With all respect...

Are you really sure you want to go to Europe? Why do you think you want to? If as you say, you really have "no preferences", it makes me wonder if you would really enjoy the trip to Europe. I'm not trying to be snarky, but just wondering what is your motivation.

Everything on your list could be done pretty much anywhere in June - in Texas, Florida, California, New Jersey - all you need to do is better define what your idea of a "spectacular monument" means to you (there are "monuments" everywhere).

FWIW, if swimming is very important, you may find yourself disappointed with the "beach experience" in Europe (I think most North Americans dream of beaches that are more like Hawaii or Mexico, and most European beaches are not at all like that).

You say you're on a tight budget, and Europe isn't cheap. Maybe someplace that's not on the other side of the world would make more sense. And IMHO "10 days" isn't really enough time for a trip to Europe for most people (especially for your first time, as you will not be as efficient as someone who has been there before) - if that includes travel time, you basically have a week of usable time there. For all the expense and effort to get there and back, it just makes sense to stay longer (but then there's that budget thing).

If you really want to go, great, do it - but before you decide, you should invest some effort in learning about what's there and how those things might or might not line up with your interests.

Choose Barcelona which has the city beaches of Barceloneta.

1. Arrive Barcelona (5N)
2. Barceloneta (beach)
3. Barcelona
4. Day to Sitges (beach)
5. Visit Sagrada Familia
6. Fly to Sevilla (4N)
7. Seville
8. Day to Cadiz (beach)
9. Day to Cordoba for the Mezquita
10. Depart Sevilla

Just a clarification: We currently live in London, so travel fees are significantly cheaper for us. Both of us have lived in Europe for a few years now, so we don't have any 'American standards'. We're quite liking the idea of Italy or Greece for now,

Italy will cost you significantly more than Greece, assuming that you would be avoiding Santorini and Mykonos.

Have you considered Croatia? The food is better than in Greece. You could fly into Split for a few nights taking in the historical sites of Split and Trogir, possibly Plitvice national park, then head to Hvar town for a few nights of partying and some great beaches with warm water and then head to Dubrovnik and fly back from there.

Just a clarification: We currently live in London, so travel fees are significantly cheaper for us. Both of us have lived in Europe for a few years now...

LOL...minor detail there. :)

Never mind what I said, I figured you were from Nebraska.

Enjoy your visit to The Continent.