Travel

Barcelona

Essentials

Get the Timeout guide to Barcelona. I used it as my bible when I was living there, it's a lot more thorough than I can be :)
The Sagrada Familia (climb to the top, damnit) and Parc Guell are amazing.
Go to the Picasso museum. Do it!
Spend a day on Montjuic: walk up from Placa Espanya, do the Olympic Museum + stadium, walk around the Olympic area and then head up to the Miro museum. Then walk to the cable car and get it down to the port.
Overlooking the city is Tibadabo, a hill with a totally corny funfair, a very odd cathedral (built by Franco's cronies to piss off the leftwing and decidely not suppportive of a nazi-rightwing-Catholic dictatorship people of Barcelona) and a HUGE telecommunications tower with an amazing view of the city and surrounding areas.
Go and check out the magic fountains at Placa Espanya. The music is shite, but they're good fun - Something to do between the daytime and nighttime stuff after eating.
FC Barcelona's stadium has a great museum, and is a impressive enough to see in it's own right. The tour gets you onto the edge of the pitch, but not actually onto the playing surface, into the dressing rooms etc., it's definitely recomended (I've done it 5 times now).
Do the modern art museum (MACBA) in Placa Angel. There's some nice eateries around there too.

Sit on the right hand side of the plane when you're flying into Barcelona, there's a great view!

Day trips

Take a train up to Figures, go to the Dali museum.
Climb up Montserrat (a train ride away).
If you're beaching, do not go down to the beaches in Barcelona. Well, you can, but they're shite and busy. Get a train down to Castelldefells or Sitges, the beaches there are natural and far more pleasant experiences.

Eating=

There are good fooderies everywhere really, follow the Timeout guide (there's a food and drink specific one). I liked Gracia, there's some great places there (look out for an Iraqi place and a Cuban place).

Mmmm, beer

Razzamatazz has multiple stories of music (mainly alternative), open late (like, until 6am or so) and is good fun. http://www.salarazzmatazz.com/
Spend a night in Placa del Sol (Gracia), Mond bar is a great indie bar, and Woodies is a cool little jazz bar.
La Paloma is a trendy nightclub in an old Ballroom.
I liked Bar Benidorm, 39 Joaquin Costa (near Placa Angel).

Rome

http://www.stargatehotels.com - Reasonably priced at high season, OK. Nice dDouble rooms in the 'Anakin Stargate' (!!) section recently refurbished. Don't bother with the breakfast.
http://www.hotelturner.com/index.htm - on Via Nomentana, 10-15 mins to Trevi fountain. Website makes it look far nicer than it is. But you'll probably spend most of your holiday in Rome walking about.

Most places are within 30 minutes walk of the main bus terminal in Rome (Termini) so could be best to find a place to stay close to there. Full of hotels and well connected, but not great otherwise.

Another option is to find somewhere in the Centro Storico (Pantheon/Piazza Navona/Campo Di Fiori). Great food, sites, pubs, and right in the middle of things. Reasonable price might be a problem. Area around the Vatican is also a good option.
You can do Pompeii in a nice day trip, although it takes some time to get there so is a full day trip. Bring an umbrella (there is no shade there, so it makes it more pleasant on a blisteringly hot day). Alternatively, do this day trip during off-season and in less heat. Also could do this trip via a night's stay in Napoli (supposdely fascinating if not relaxing), and/or another in one of the towns along the Amalifi coast such as Positano or Amalifi or Ischia.

Alternative day trip possible to Ostia Antica, the Roman river port. Adam (cthulhu) recommends it as just as good as Pompeii but less than an hour from the city.

Sistine Chapel is morning opening only, and queues are massive so get there early. Not all brickies recommend this, as there is a long walk around heavily decorated corridoors through crowds before you actually reach the chapel, and it has the potential for anti-climax. (Alternatively, it is still quite impressive!).

Other options for visits include the Colesseum and the Palantine (both covered by the same ticket, you can save time if you buy at the Palantine).