General business hours in Japan are weekdays 9-5. Many offices also open at least half the day on Saturday, but are generally closed Sunday.
Banks are open weekdays from 9 to at least 3, some now staying open until 4 or 5. As with shops, there's a trend toward longer and later opening hours.
Gas stations follow usual shop hours, though 24-hour stations can be found near major highways.
Museums generally close Monday and the day following national holidays. They are also closed the day following special exhibits and during the weeklong New Year's celebrations.
Department stores are usually open 10-7, but close one day a week, varying from store to store. Other stores are open from 10 or 11 to 8 or 9. There's a trend toward longer and later opening hours in major cities, and 24-hour convenience stores, many of which now have ATM facilities, can be found across the entire country.
As elsewhere, peak times for travel in Japan tend to fall around holiday periods. You want to avoid travelling during the few days before and after New Year's; during Golden Week, which follows Greenery Day (April 29); and in mid-July and mid-August, at the time of Obon festivals, when many Japanese return to their hometowns (Obon festivals are celebrated July or August 13-16, depending on the location). Note that when a holiday falls on a Sunday, the following Monday is a holiday.
Japan's national holidays are January 1 (Ganjitsu, New Year's Day); the second Monday in January (Senjin-no-hi, Coming of Age Day); February 11 (Kenkoku Kinen-bi, National Foundation Day); March 20 or 21 (Shumbun-no-hi, Vernal Equinox); April 29 (Midori-no-hi, Green Day); May 3 (Kempo Kinen-bi, Constitution Day); May 5 (Kodomo-no-hi, Children's Day); the third Monday in July (Umi-no-hi, Marine Day); the third Monday in September (Keiro-no-hi, Respect for the Aged Day); September 23 or 24 (Shubun-no-hi, Autumnal Equinox); the second Monday in October (Taiiku-no-hi, Sports Day); November 3 (Bunka-no-hi, Culture Day); November 23 (Kinro Kansha-no-hi, Labour Thanksgiving Day); December 23 (Tenno Tanjobi, Emperor's Birthday).