November--great time. I had originally planned October for the weather supposedly around the 70's but was too busy at work and postponed it to Nov. The weather was beautiful, it is one of Japan's least rainy months. During my entire month it only rained 5 times tops lasting only about 5-10 min and was was more of a sprinkle. One night while wandering in Ginza it rained for a hour, but I had a hood and it still wasn't super heavy. That didn't stop the girl from the pachinko parlor running out to give me an umbrella as a gift...things like this will happen in Japan.
It was usually sunny and around the 60's I got by simply wearing thermals on the colder nights. I did not pack a heavy jacket nor found a need for one. Do not pack too much, make use of layers if it is needed at all.
*Visa is not needed...your Passport grants you 90 days by default as a temp visitor.
*you could easily get by at $500/person +CC when possible. Tokyo is not that expensive (I am from Socal so that may skew my perception) New york in my opinion costs way more. Most things(especially as a first timer) cost very little or are free as you are just amazed with walking down Takeshita dori.
*YOU WILL GET LOST. However, Japan is probably the least scary place you will ever visit. Never once did I feel unsafe wandering around at night(one of the few places I would even tell my sister, its ok to go solo). Tokyo seems to always be busy with lots of people no matter what hour of night. Just know how to say, "Sumimasen, <Place> wa doko des kaw?(spelled how it sounds) this will usually get you a point in the right direction or if you look really lost a guided walk to your destination.
Bring a compass it is invaluable just to know which direction you are facing so you can quickly orient yourself to the maps(tons of maps available once in Japan). Tokyo is a maze, even the locals can rarely figure out where a place is by an address...so you can forget trying to make sense of an address.
So again you will get lost but it's not like LA where its a really bad thing to be lost. The people are super helpful and nothing a compass and a tourist map cant help remedy.
I recommend the Ninja Khaosan hostel its close to the trains and Asakusa is a great part of Tokyo.. easy walk or train ride to Akihabara and easy to get to Chuo line to hit the other side of Tokyo. If you want more privacy you can get a room at the Shinjuku Sunroute plaza for about $100 usd a night if you stay 7+ nights it is in a great location and is really nice for the price.
If you have any other questions just ask...