Exit time depends on a number of factors, including class of service. Traveling in F or J on UA, I have made it through and down to the train station in 15 to 20 minutes, but I cut the time down by only having carry-on luggage, having my money already in hand and knowing exactly where to go. I have yet to be examined at Customs. They just wave me through. When traveling in Y, it always takes longer as you won't be at the head of the line at Passport Control. My flights always arrive in the afternoon, so I am not familiar with the morning arrivals but if several flights arrive at the same time, the lines to get through immigration can get pretty long. That all said, I can't imagine taking more than 45 minutes to an hour. You can cut the time by getting cash at an ATM rather than an exchange window and the line at the Keisei ticket window is always shorter than that at JR, right next door. Figure you could be on the train platform in an hour or so, could be less. The Skyliner is pretty fast and will get you to Keisei-Ueno in less than an hour.

All the above is a bit beside the point as the first Skyliner doesn't depart until 8:17 am, arriving at 9:15 am. There are a couple of earlier trains but they are slower and would only save 6 to 9 minutes. Plus some of the options involve a change from train to subway at Aoto, which I don't advise for a first-timer. I'd say take your time, get your tickets and then look around NRT a bit, maybe buy some snacks for the morning (I must have my bottle of green tea for the ride) and be a little less rushed getting on the Skyliner. There is a return Skyliner at 13:40 which arrives back at Terminal 1 at 14:23. The next earlier one is at 13:00 and the next later at 14:00.

Getting back through security at NRT Terminal #1 is very quick and painless. You may have time to do some shopping, eat or check out the observation deck.

All that to say, using the most comfortable and easy travel options, I think your actual time in Tokyo would be 0915 to 1340, a bit less than 4-1/2 hours. If it were me, I'd purchase my return tickets upon arrival at Keisei-Ueno, exit and immediately go up the steps to the park and stroll around, looking for pictures. The National Museum (and several others) are toward the back of the park for a place to get indoors. After that, I'd walk through Ameyoko, avoiding the foreigners selling fake phone cards and whatnot. Then, assuming it is after noon, I'd go across to the Ueno Station area to find a likely spot for lunch and then head back to Keisei-Ueno for the ride back to the airport. Alternatively, you could forego the park and instead find the Ginza Line subway station and go straight to Asakusa, walk the old town or Nakamise Arcade, visit the Senso-ji Temple complex and find some lunch in Asakusa. I might just graze the food stalls on Nakamise instead of a restaurant but either would be good. Then return to Ueno on the subway, walk across the street to Keisei-Ueno and return to the airport. Doing both Ueno Park/Ameyoko AND Asakusa in 4-1/2 hours would be rather rushed and hectic. If you want to try it anyway, I'd suggest going straight to Asakusa upon arrival at Keisei-Ueno, leaving Ueno Park for whatever time is left on the way back.