Right, so you're from London. One of the top attractions in Kobe is, ironically, a concentration of Western-style houses(!). But that's probably not going to be a huge attraction for you. However it's claimed by many sources, including Wikitravel, to be the must see attraction, so if you want to, head to the Ijinkan - near the Shin-Kobe station. These are 19th-century residences of Kobe's foreign traders, clustered in the Kitano area.
To me, Kobe immediately brings to mind images of their terrible earthquake in 1995, which killed 6433 people. If you head to Meriken Park, they have a memorial there to this.
Just nearby is Kobe Tower, which has a viewing pavilion, so you can get a good view of the city.
There's the Fruit Flower park, but it's not really going to have too many blooms in February. Same for the Herb Park.
Ah, now to drink - Kobe is known for its sake! In the Nada area are breweries, so I'd try and head there for some tastings :) The Hakutsuru Sake Brewery Museum has free entry, and free sake!
At night, you mentioned the Kobe Luminaire. However, note that it's generally only in December, and even then only on certain days. Check when you get there though, as it may be running for a special event, and it'd definitely be worth seeing.
Oh! Also, try and find some Kobe beef. Oh now I'm jealous, I totally want to try it from there. "The meat is generally considered to be a delicacy, renowned for its flavour, tenderness, and fatty, well-marbled texture.".
Now, Tokyo. This will be your history stop (Kobe was more food and culture?). You'll need to go to the temples of Asakusa, the gardens of the Imperial Palace, and the Meiji Shrine.
If you're looking for a view of the city, you have a few options. The Tokyo Tower is the obvious one, but expensive. Alternatively, head to the Tokyo Metropolitan Government building. It's the highest spot in Tokyo, and has viewing platforms, and is FREE! A final option is considered to be the best, however, from the World Trade Center Building at JR Hamamatsucho station which, "although not as high, offers stunning views of Tokyo Tower and the waterfront due to its excellent location, especially at dusk".
I'd also do a sento (public bath) experience, and go to Shinjuku at night - the lights are supposed to make Picadilly Circus look like a backwater town!
There are also several museums in Tokyo, so if you want some more history - Samurai or art or other, check out the list of them when you get there, I won't bother listing them out here. The National Museum looks to be the most relevant for a tourist to go and enjoy though, from what I can see.
