I have stayed at all 3, previous to my stay at the New York, the Newport Bay Club was my favourite, I love the NPB, I think it's the most beautiful of the hotels and the theming and the colours are very appealing, we had an unforgettable stay there and in terms of customer service and extra Disney magic this was our most memorable trip. We had booked the Admiral's floor, had a free upgrade to lakeside rooms, son had lots of freebies for his birthday, we got upgraded to a VIP breakfast, which meant we had a private breakfast room and the whole stay was unfaultable.
I've had 2 less than perfect stays at Sequoia Lodge, but that was prior to the refurbishment and I'd be happy to try it a 3rd time, as most of my gripes came from the tatty rooms, although it is the only hotel where housekeeping has been almost non existant. I don't like the look of the Sequoia Lodge at all, I don't like the dark wood inside and think the building is ugly, I don't need the tall pine trees and bird song, I'm fortunate to be surrounded by them at home.
I've stayed in the main building and in a lodge, the lodge was my favourite, it was a shorter walk to reception and to the parks than our room in the main building.
The Hotel New York, never wanted to stay here then got the opportunity and yes it is a "cut above" the rest, the proximity to the park, we always walk regardless of which hotel we stay in, but being so close it was easy to pop back in the daytime. We did get upgraded to a lake view room here too
There's something about the ambiance of HNY which makes it that bit posher, if that's what you want, I wouldn't say it's particularly child friendly in theming but then if you want child friendly you can't beat the Cheyenne (cowboys) or Santa Fe (Cars fans).
HNY has the best breakfast with a hot selection included, pastries and cakes as standard and the largest selection of yoghurts including low fat varieties. Hot breakfasts are available for a supplement at SL and NPB if you want them.
I'm not sure quite why but if I were given free choice of hotel, (someone else paying) then I would choose HNY out of the 3, think the neighbours being Cafe Mickey help swing the decision
In my experience of walking distance it's HNY, followed by NPB and then the SL if you're staying in the main hotel, if you're staying in a lodge and can get Yellowstone, that one's just around the corner from HNY, you have to find the small path through the trees.
If you're likely to use the swimming pools I believe the SL has the best one, although I like the look of the outdoor NPB one, obviously just for Summer trips, but we have never found the time to use the pools.
I have the Cheyenne booked for our next trip, with the intention of changing hotel when a 40 or 50% deal comes out, HNY would probably be my first choice, but then the NPB as it's a summer trip and think the hotel has a summery feel, we did have a March trip booked which we had to postpone that was at SL because of it's wintery feel. My husband thinks I'm mad BTW for my reasonings on the hotel bookings.
Sorry if I've rambled but everyone has their favourites and I think it's a good idea to know why people like or dislike a hotel, if you have a bad experience it tarnishes your view a good one does the opposite. What I don't like and it happens a lot with the NPB is when people who haven't stayed there knock it, I know from previous discussions on here that the majority of DISers who've stayed there have loved it.
Don't pay too much heed of Trip Adviser, I sometimes wonder if I've stayed in the same hotel as the one's being reviewed on there, again I think people tend to use it to complain rather than praise - just my humble opinion. Wherever you stay for a first trip I'm sure you'll have a great time, on our first couple of trips I'd have stayed in a garden shed if it had meant a Disney trip.
) but I'd go for the SL.
Enjoy all the planning! 
