You will be staying in Asakusa but running all over the city to see major sites? Asakusa IS one of the major sites. You can walk to and around old town Asakusa, see the old entertainment district or the food/kitchen supply street, visit the important Senso-ji temple complex, shop the Nakamise-dori arcade, take the water taxi down to Hama Rikyu Imperial Garden. From there, you can walk to Tsukiji Market or Ginza or even take the water taxi back to Asakusa.

My point is that from Kuramae it is one stop on the subway to one of the more interesting old neighborhoods (Asakusa.) Also from Kuramae, on the Oedo subway line, you can get to Ryogoku (sumo town) in only a few minutes to visit the Edo-Tokyo Museum or have a meal in one of the many little restaurants. Two stops on the Asakusa Line subway from Asakusa Station will get you to Ueno and the Ueno Park complex of the National Museum and the delightfully seedy Ame-Yoko shopping arcade.

Cheap meals are found on every corner and side street in Asakusa or Kuramae. Just walk until you see a window display that looks inviting. For real budget meals, a big bowl or ramen is hard to beat.