1)...what to do on New Year's Eve 2003? I guess we'll just walk the Ramblas,

Don't know about Barcelona, but I imagine they have "macrofiestas"
just like in Madrid, public events for which one buys a ticket and
gets to celebrate New Year's Eve with a bunch of people one doesn't
know.

2) I'll be renting a car and leaving Barcelona for about four days.
Have to get back to the airport there, so can't go more than a 4-5
hour drive. Any suggestions of interesting towns, villages, moderate
hotels for my several days?

You could drive to the Pyrenees (Aigues Tortes National Park), you
could hang out in the coastal town like Cadaqués, you could visit the
Museu Dalí en Figueres, you would visit some neat Romanesque towns
like Besalú, you could stay in Olot and walk the volcanic areas (one
cone has a church inside of it). There's lots to do in Catalunya. The
only thing that might be difficult would be to see the ruins at
Ampuries as it might be closed.