OK, with a rollaboard, this is what I do all the time:

Instead of JR from Narita, take the Keisei line to Hibiya. It is cheaper and never crowded. In fact, if you don't mind a subway-type car they have limited express trains for just 1,000 yen (the faster SkyLiner is about double that).

At Ueno you roll down to the Hibiya line (note there are about 10 stairs is all along the way). It is very well marked in English... you can't miss the underground passage. When you get to the Hibiya line (not Ginza line) area, buy your ticket directly to Ebisu and head left toward the elevators. You will go thru the turnstiles, onto the elevator, and directly to the platform.

At Ebisu you will go up to ground level (I think there are elevators or escalators, if not there are not many steps), and it is all escalators and moving walkways from there to the Westin.

Why this makes sense vs. taking JR:
1. Keisei is not only less money but almost always empty; you have your pick of the seats as opposed to sometimes having to wait for another JR Narita Express train during peak travel seasons such as now.

2. You almost always get a seat on the Hibiya line at Ueno vs. the crowds you have to contend with at Tokyo JR station when connecting with the Yamanote line

As others have mentioned, trains are the way to go when it comes to Narita, unless you have a lot of baggage. Also, be aware that next week is the "Obon" holidays in Japan so everything travel-related is going to be chaotic!

Have a great trip!