Hey, Good to hear about your trip to Spain. Barcelona and Palma de Mallorca are beautiful places and so is Valencia. Lets take up your questions one at a time. Let me start with the Palme de Mallorca itinerary.
Explore Palma de Mallorca
There is lots to do in and around Palma de Mallorca. Museums, Cathedrals, Beaches, Nightclubs and lots more. Let me give you an idea of how you can spend your two days.
Day 1 : Visit the museums and Castles. Start your day with a visit to the Gothic Catedral de Mallorca which is the landmark of the city. The Cathedral dominates the waterfront and is located in the oldest part of the city and also has a museum which has exhibits of religious paintings and silverware. The msueum opens at 10 a.m. and closes at 5:15 p.m. on weekdays and 2:15 p.m. on weekends. Now, head on to the Castell de Bellver which is a beautiful well preserved fortress dating back to 14th century. Located on top of the wooded hill, it offers spectacular views of Palma Bay. It is open from 8 in the morning to 9 in the night on the weekdays and from 10 in the morning to 7 in the evening on weekends. Another attraction for the day is Banys Arabs is the only building which dates back to the Arab era. It is an Arab Bath building which was constructed in the tenth century and the baths were Sauna style. Some baths are still open to public and for the entrance, you are expected to pay 2 euros.

Source : Sai Rodriguez/Flickr
End your day at Paseo Maritimo which has a fantastic nightlife. There are a lot of clubs along the ocean in Palma which are open till 6 in the morning. The parties start only by midnight. The view of the sunrise in the morning is spectacular from the island.
Day 2 : Beach bumming, Golf and Drinks. There are quite a few beaches in Palma. Besides the sand beaches, there are a couple of pebble and rock beaches also. The best public beach is Playa Nova which is about 35 mins from downtown Palma. The swimming is ideally enjoyable in the months of June to October but if you don't mind a little cold, you can sure take a dive. You can also head to the golden sand beaches at El Arenal which are very well equipped with all the tourist facilities.
Majorca is a golfer's dream. The best golf course is Son Vida Club de Golf, Urbanización Son Vida which is about 13 kms from Palma. It is an 18 hole course and reservations are strongly recommended. The fees is about 80 to 90 euros. For more information visit this website.
When the sun sets down, find your way to Tito's for the best drinks and to mingle with the best international crowd at the terrace which overlooks the Mediterranean. The disco here is known to have witnessed the most wild parties ever. Dance through the night and have fun. It is open from 11 p.m. to 6 a.m. from Thursday to Sunday. You can also read this article which talks about nightclubs in Mallorca.

March 27th is a day when the whole island is partying at some place or the other. Quite a few festivals and events are celebrated on this day. I don't know your time of arrival in Majorca but if you are arriving in the morning, then you can be a part of some of these festivals.
Driving Directions and Car Rentals
The drive from Valencia to Barcelona is a short drive of approximately 3 to 4 hours. There is a fast motorway as well as long sightseeing routes. If you have a day to drive from Valencia to Barcelona, then you can take the longer scenic route. The travelers who have been there earlier don't recommend this route because of some traffic jams in the tourist season. What I have done is created a basic route map for driving to Barcelona on google maps. The map has driving directions and pictures also. 349 kms in about 3 hours and 30 mins.
I also found this website which gives you options to plan your own route. You can see the quickest, shortest and sightseeing routes with just a click. All the routes are very clearly explained and the map has all good hotels, restaurants and sight seeing places clearly marked along the route. You can either choose to rent a car or find a good deal with these guys. Whichever route you take, you will have to pay a toll free which is approximately 34 euros and the petrol cost should come around 33 euros. These guys have been recommended by a lot of other travelers. You can go through this forum to read more about the drive from Valencia to Barcelona.
There are many operators which let you confirm your bookings online. People who have traveled earlier recommend Europcar, easyrentacar and Hertz. The hotels where you are staying in Valencia can also help you in renting a car. Also, if you ask some local people there you can find some good deals.
I am sure you can find the best route if you spend some time going through each of them. Now that we are done with the car rentals and driving directions, lets get to the next question. I guess you want me to help you with the itinerary for 2 days in Barcelona. Let me give you an idea of what you can do in Barcelona.
Barcelona in Two Days
Barcelona is fun at any time of the year and has something for people of all ages and interests. Your two day trip will be an interesting palette which will be mix of a bit of histroy, generous amounts of fun sprinkled with a dash of music and some mouth watering food. Visit the many museums, have a look at the historical statues and archways, take a break and visit the operas, do some shopping and lots more. I really like the two days itinerary from Frommer's. They have also recommended some nice restaurants and bars. What I have done is created a Flickr slide show to give you an idea of what you should expect on your trip to Barcelona.
Nightlife
Barcelona is very fashionable and trendy and has a pulsating nightlife and is a home to some of the best pubs and nightclubs of the world. The party scene starts at 8 p.m. but the clubs will have almost no crowd till 11 and this is the time when the splurge comes. The parties begin by 11 and are on till midnight. Some of the best clubs don't even open before 1 a.m.
One of the best clubs is La Paloma which is known for old style dancing and for its age. It is 105 years old but still very young. In the evening when it opens, it is a place for music lovers. Come midnight and it becomes a hip place where you can dance through the night and party till morning 5 a.m. Another popular place is the Bikini which opened as an outdoor bar and is a popular place for some lively dancing. Frommers also recommends this place. Here is what I found :
It is now a venue both for live music and for lively dancing. One room is Latin rhythms, another disco/punk/rock/whatever's going, plus a chill-out cocktail bar tucked away as well. It's also one of the better places to hear live music; when the gig's over, the walls roll back and disco rules.
La Terrazza, La Boite, Jamboree and Razzmatazz are some more places which you can try out. Frommer's also has this interesting write up on nightlife in Barcelona
Hope the above information helps. If you need more details about the itinerary or night clubs, please do write back and we shall find it out for you.
Did you know that Barcelona has some very beautiful places where you can plan your stay. So while you are deciding what to do in barcelona, why not find out some hotels too.
You can post your next question for hotels right away.
Happy Planning!
Sneha.
Mar 23, 2010