I believe you should be fine. The basic expenses are for a simple double business hotel room 12,000 Yen/day, nutrition 4,000 Yen/day and person and transport 1,500/day and person. Then add 2,500 for transport from and to Narita on the cheapest Keisei ticket to Ueno and you end up with 281,000. You’ll have an extra 25,000 yen for public baths, gardens, museums and contingencies. Obviously going up on the Skytree etc. and will eat up your budget very quickly.
You can find cheaper rooms. Some years ago I was always able to find something nice between 6,000 and 9,000 Yen. My favorite chain back then was TokyuStay. That is not the case any more. However I still know a very simple, clean place for 4,000 Yen in Asakusa and a tourist friendly ryokan in Nezu for about 6,000 Yen for a single person.
If you want to take a break from Tokyo you can take the bus from Shinjuku to Fujikawaguchiko and stay at the Kawaguchiko Station Inn. The have unbeatable off season rates and you can easily spend a couple of nights there and take in the scenery.