From Yanesen to Asakusa
To go to Asakusa, taking the bus is the easiest way. You can take a Toei bus (Tokyo city bus) No. 63 at a bus station at Dangozaka-Shita near Sendagi station. The bus takes you just in front of Kaminari-mon, (The entrance of Sensouji Temple). It will take 35 minutes or so. Going to Ueno station by walking is also possible. From Ueno station, you can take the Ginza subway line and Asakura station (G13) is only 3 stations from Ueno.
From Yanesen to Ueno and Akihabara
It is not impossible to go from Yanesen to Ueno or even Akihabara by walking. I have walked from Nezu Station to Akihabara and it took me about 35minutes. Ueno is much closer and it takes about 15 minutes or so.
From Yanesen to Harajuku
By taking the Chiyoda subway line from Sendagi or Nezu station, you can go Harajuku. To go to Harajuku, get off at Meiji Jingumae (C03).
From Yanesen to Imperial Gardens
Take the Chiyoda subway line from Sendagi or Nezu station and get off at Otemachi (C11). It takes about 15 minutes.
From Yanesen to Roppongi Hills
You can reach Roppongi by Chiyoda subway line. Take the Chiyoda subway from Sendagi or Nezu station and get off at Nogizaka station (C05) It takes about 25 minutes. From Nogizaka station, you can walk toward Roppongi Hills. It will be about 10 or 15minutes walk.
From Yanesen to Shinjuku / Harajuku
Take Yamanote line from Nippori station. To Shinjuku, it takes about 20minutes. To Shibuya, it takes about 25minutes.