I am glad to hear that you are okay with seafood. Then, you will have so much fun with sake bars
Regarding the facility tour, I haven't done for JAL but I have been to the ANA one. (I prefer NH to JL) It's free and it was about 1.5 hours. You make a reservation on their website.
http://www.ana.co.jp/cp/kengaku/tours.html
Then, you will have to fill out the questioniare to get the admission pass which will be e-mailed back to you.
First, after the security check, you will have to present the goverment issued ID as well as the admission pass. You get to go to the classroom like room to hear about all the hardworking NH people and how maintenance is conducted. Then, you will be instructed for what you should do and shouldn't in the facility. You will be taken to the "changing room" and wear a helmet and you will be seeing the aircraft parked in the facility.
If you are lucky and sign up for the tour by NH, you migt be able to see 787

However, it was 747-400D in my case. You are able to take a lot of photos but I don't think you can touch the aircraft. You will be taken back to the reception area 50 mins after and there is the little souvenir shop in there. You are not obligated to buy them if you don't like them.
Anyway, all of this will be done in Japanese unfortunately. If you do not care about what they have to explain to you, I guess you wouldn't have too many problems but it's better to have a translator. The free translators are not too great but they can speak basic English and this is something you might wanna look at
http://tokyofreeguide.com/. If it's not a weekday, I can totally go there with you. I personally think NH is better than JL as they have more wide bodies. (They still have 747s for domestic routes) This tour thing gets filled up pretty quickly so the earlier you make a reservation, the better.
As for a spa, Edo Onsen Monogatari is very touristy and it's great. But if you wanna try some day trip to the south, there is Enospa on Enoshima island. You could go there after visiting Kamakura (Hokokuji is a must stop in Kamakura as it's fantastic but you will get more "sacred" feeling when it's in the early morning around 9.). If the weather is nice, you will be able to appreciate Mt. Fuji at the same time. Highly recommended.
http://kanagawareviews.blogspot.com/...-enoshima.html
Anyway, I hope this will help a little bit.
Good day!