First and foremost,
SELAMAT DATANG, CrazyT!
Welcome to Malaysia!
(Puts right palm over heart, and bows slightly. Yeah, that's the way to do it here when we want to be really nice to foreign visitors ).
According to your post #4, you'll be staying in a hotel. I supposed that will be for the entire duration of your 3-month trip. Find out where your hotel is located. If it's in a central location, you won't have to worry about going shopping, eating and hanging out. Everything should be within a stone's throw then. If not, taxis are good, especially the metered ones in the city. Try to avoid those who refuse to use their meters, as they tend to be ridiculously exorbitant for terribly short rides.
What locals do for fun (in your post #4):
My idea of "fun" - eat, sleep, shop, eat, sleep, sleep, sleep, sleep .... (ok, it's an inside joke).
Anyways, the best thing about Malaysia from a local person's point of view is the food. I've lived in various countries for more than 15 consecutive years, and in each of those years, the first thing I do when I return for a visit is to eat, eat, eat!
Hoju mentioned Jalan Alor in post #12. There's good news: it's still called Jalan Alor (literally, Alor Street). The renaming exercise was met by vehement protests from residents and visitors alike. Anyways, visit Jalan Alor as often as you can, so that you can try everything (or almost everything) there. It's almost like the best-known foods of Malaysia, all in one place.
You should really plan to visit other parts of Malaysia, instead of remaining in KL throughout the duration of your stay.
Places you should go to:
1. Penang (up north from KL, about 4 hours by coach) - it's been named a World Heritage Center recently, so there's quite a bit to see if you're into history and stuff. And the food is great. It's somewhat different from what you'd get in Jalan Alor, although there might be some similarities in visual form and name.
2. Melaka (down south from KL, about 2 hours by coach) - another place packed full of history ... and more good food, with a different twist/taste.
3. A beach-type place. If you want to save time/money, go to Langkawi. It's not too far away from Penang, and full of legends that can make your skin crawl, if you're into that kind of stuff. But it's not really a creepy kind of place; don't worry. You can also get a variety of duty-free stuff there. If you have money/time, go to Sipadan in Sabah and scuba-dive. Hoju (and everyone else who's been there) will tell you that it's definitely worth going.
4. A couple of local festivals/events. Check with your hotel for local festivals/events (e.g. sports, cultural, arts, etc) that you can attend while you're here. If you can, try to catch/attend the national-level open-house Chinese New Year celebration. You won't find such celebrations anywhere else on earth, and here in Malaysia, we do it at least 4 times a year!!!
One final note: You're here on a business assignment, so work should get more priority than play. So don't fill your free time with too many recreational or entertainment activities, as the unexpected hiccups (sudden downpours, traffic jams, miscommunication with locals, etc) can occur and cause you to be late for work etc and basically throw a spanner into things.
Enjoy your assignment here, and take in some of the sights/fun. If you like it, you can always come back. We will always welcome you!