I stayed in 新宿 Hotel Vintage before, small room but just ok for taking rest over the night. 新宿area has advantage for "夜鬼", some 24 hours shops are around.
I can't comment on 池袋 Theatre Hotel as I never stay there before.
I haven't stayed at Vintage before, but I have been staying in Hotel Theatre this year.
Rooms are clean and nice for hotel theatre, but not big rooms. You need to take about 7 mins walk to the JR station.
However you can choose to take the limousine from the airport to Sunshine City Prince Hotel, and from there, you need around 7 minutes to get down to the hotel. I left my baggage with Sunshine City Prince in the morning, after checking out with Hotel Theatre, and continue shopping in Sunshine city until taking the limousine in the afternoon.