If you decide to go to Nikko, you may want to use on of the many Tobu Nikko passes. There are ones with different lengths of usage, and some have theme park passes bundled in with them:
http://www.japan-guide.com/e/e2358_002.htmlThe Tobu train takes about two hours to get to Nikko.
The Tobu line runs from Asakusa to Nikko. If you are looking at Hyperdia to figure out times, use "Asakusa(Tobu/subway)" as the start, and "Tobu-Nikko" for the destination. The Tobu pass will only use Tobu trains, and I notices that some of the Hyperdia routes showed the green JR trains, instead of the pink trains. You may need to narrow down the search by limiting the trains to only private railways (There is a box to turn off JR trains).
To get to Asakusa from most places in Tokyo, take the Yamanote loop line to Ueno Station, and switch to the subway.
If you do get one of these tickets, you will have transportation back to Tokyo, but not to Narita. I looked at the transportation page for Narita Airport, and Asakusa is shown on the map:
http://www.japan-guide.com/e/e2027.htmlIt looks like you will take a subway from Asakusa(Tobu/Subway) Station to Aoto Station, and then switch to the Keisei main line to get to Narita. If you want to use hyperdia for route information, the destination station for Narita will be "Keisei-Narita". The cost is just under 1000 yen, and takes just over an hour to get there.
Firas has a great suggestion for a bus directly to Narita Airport, even if you have one of the Tobu Passes, you might want to use this for convenience.
Good Luck, in planning your trip.