So you are only staying at a hotel one night and are staying near Newport for the rest of your stay? Not staying at one of the good neighbor hotels? Who will be with you? Are you checking in at 3 because that's check in time, or because that's when you're arriving in the area?
If it's just because it's check in time, I definitely agree -- go earlier. You may be able to check in earlier, but even if you're not, go to the pools, etc. Limiting your time at the hotel from 3 to evening, then going to DCA the next day is not a lot of bang for your buck at these prices. We have done a DLR hotel one night in the past -- but the way we did it, our non-park day was the day AFTER we checked in, so we had all day for the hotel, DTD, etc. They will hold your luggage for you at the hotel. If you wait until 3, you'll probably be headed to a very busy pool, btw. If you use the hotel amenities on a non-park morning, the pools will be less crowded and you'll have all day.
Anyway -- which one really depends who's with you and what you want to do. I've stayed at all 3. Obviously the GCH is closest and VERY convenient to DCA. If you have the $$ and are without small children, I'd probably go that route, particularly since you'll be at DCA the next day. Not sure what they're doing for the renovation, but the pools there have always been a bit more grown-up feeling than the other two properties. The common areas (lobby, etc.) are beautiful and you'd be close to Napa Rose if you want to do that. I think Napa Rose is easily the best restaurant in DLR. OTOH, if you have younger kids with you, I'd do the DLH. It's more "fun" feeling than GCH and kids love the pools there ... but they can get quite crowded in the afternoons. For the adults, Trader Sam's is a lot of fun as well. And kids can go to TS during the day. Personally I'd avoid the PPH, although I know there are some here who like it. To me it just doesn't have the magic of the other two hotels. It feels like a very average hotel that has some Disney branding stuck on it. Although you can get a GREAT view there of DCA for much less than you can at the GCH.