hi justinlee
i did my first trip to japan last year thinking the same way as you.
i wanted to see the blossoms.
first thing i did was to search out that web site with the expected opening of the blossoms and planed my trip from there.
When i arrived Tokyo it was in full bloom while kansai area hadnt started. So i spent a few days in tokyo going to the big parks there. While nice i still found it to be to many people :)
i then activated my railpass and started going all over the country to find the blossoms. The information center in Kyoto was really helpful in pointing me to places in full bloom.
But a tip is to go to the big castle towns ( himeji, osaka, nagoya kumamoto etc) around the castles there are often alot of blossoms.
i visited over 50 castles so its a safe card :)
As of budget. I spent 3months in japan. first 2 i was traveling constantly and the last i stayed in tokyo.
i forced myself into a tight budget about 8000yen/day. i dont think you can go much lower than that.
The railpass is a must if you are going to go to different places. i used the 3week one. then you end up with about 3000yen/day in travel cost.
in the big citys i most often went into the capsule hotels. they are unexpensive (about 3000Yen) ,central and dont have a curfew as some hostels.
As i was going to do some hiking i had all my outdoor stuff with me so i also spent alot of nights tenting ,that cut down the costs :)
i dont think you can get under 2300dollar/month.
as of language i didnt have any ( ok some..) problem getting by with just simple japanese words as ''when'' ''where'' and so on. just keep a notebook in your pocket so that train station personal can write down trains,times ,changes etc.
when going to small places the arrival time is the only thing you got for going of at the right place cause there are no english signs and sometimes the speakers arnt that clear. Lyckely you can most often set your watch after the japanese trains :)
more tips on places can be found on this site where i have uploaded some pics.
http://www.resedagboken.se/search for ''Fluppo''
hope this helps