I vote for four days in Washington D.C.. You might want to consider going to Philidelphia on another long weekend. It's a great city. Are you aware most museums are free in D.C.?
I definitely vote for 4 days in DC, would go longer if you can...but I enjoy Philly too.
It's up to you. I think one thing to factor into the equation---if you devote the 4 days to one city, do you think at some point you will be able to visit the other city? If you think that this will be the only chance you get to visit both DC and Philadelphia, then spend 2 days in each.
The cities are very different and each has it's own delights. DC is, for most people, a museum/monument experience. I'm not saying there's nothing else to do there, just that most people spend their time in museums or seeing monuments. Philly has some excellent museums too, but it's a different experience (and if your interest is primarily museums, then DC wins hands down). First of all, it has a residential feel to it, almost everywhere you go will be in or near neighborhoods where people live and that gives it a charm that is different than DC's. Second, Philly is about colonial US history with many 18th century buildings still standing, in use and open to the public (DC has few such buildings, as far as I know).
With all that said, though, you can easily spend 4 full days in DC.
"First of all, it has a residential feel to it, almost everywhere you go will be in or near neighborhoods where people live and that gives it a charm that is different than DC's. "
A funny response - in a sad kind of way! People do actually live in neighborhoods in Washington DC! Most tourists don't seem to be aware of this, but outside of the monument & museum zone are many lively unique neighborhoods where real people live in real houses, with kids and schools and neighborhood pubs and farmer's markets and everything.
I'm not sure how the travel time factors into things (how much time will be wasted going from DC to Philly). But I think you can hit the highlights of Philly in 1 day (Liberty Bell and Independence Hall). So I might consider 3 days in DC and 1 in Philly if this is likely the only opportunity to visit the area.
The suggestion for 3 days in DC and 1 in Philly seems like a good idea.
Another question/ comment: how are you planning on going from DC to Philly? Do you intend to drive, take Amtrak, take a plane, or none of these?
IF you are not driving, taking Amtrak to Philly might be a worthwhile idea to consider (given you do not have too much luggage).
i would not split 3 days in dc and 1 day philly - a lot of traveling starts and stops, checking into 2 hotels over a long weekend? doesn't make sense. 4 days in DC would be the recommendation and then go back to philly another time.
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