I'll second the "no tipping" advice. It is actually a bit rude to try to insist.
Also, be aware that June is the rainy season. Be prepared for a lot of it off and on during your stay. If you get caught without an umbrella, pop into any convenience store - 7-11, Lawsons, Family Mart, several others. They will have throw-away plastic umbrellas for a couple hundred yen (less than $2.00.) "Konbinis" are located in almost every block.
Cabs are safe, honest, clean and not unreasonable for business travel. One tip, try to have a card or brochure with the address in Japanese for the places you are going, or at least have the hotel concierge write it out in Japanese, to show the cab driver who may not speak much English. Likewise, grab a card or brochure from your hotel to make it easy to get "home." Most cabbies will know the names and locations of major hotels in English but it helps to have something in writing, just in case.