We stayed at the Best Western Hotel Millennium last May. It's not far from Las Ramblas--about a 15-20 minute walk (less than a mile). Our rate was about 130 Euro a night. It's a fairly new hotel and very clean with smallish room and huge bathroom; also included is a nice breakfast buffet. I'd recommend it for your overnight stay. You can check them out at <http://www.bestwestern.com/prop_92203>
Another possibility is Hotel Ramblas Barcelona. We looked it over and it's a very nicely renovated hotel at Ramblas 33, overlooking all the action. Very nice bar and restaurant. Rate is about 150 Euro a night. They have a web site at <http://www.ramblashoteles.com/>
If you can get a "special" you might want to look at the Hotel Majestic... it is an elegant hotel and pretty expensive, but sometimes has deals. More info at <http://cruisediva.com/hotel_majestic.htm>
Any of the hotels will call a taxi for your trip to the airport. They can also advise you about the amount of time you need for check-in, etc. We find they are very attuned to that in Barcelona.
Hope this helps!