When I am in a new place for a short time: I try to get a history of the place, absorb the culture (as much as is possible) and in particular see the architectural highlights.
I would do an architectural tour (move around in taxis to zip around). KL has an abundance of its physical examples of its Colonial past that are thankfully not over-preserved like those in its neighbour to the south (everytime I see the Raffles Hotel I want to roll my eyes).
1) Sultan Abdul Samad building - this where the High Court is located. Great Moorish archiceture.
2) Then look at the big field across (Dataran Merdeka) and the resplendent Royal Selangor Club.
3) Dayabumi Complex. Islamic-influenced monolith that used to house Petronas' offices. Looking at it makes you wonder how they clean the building.
4) The nearby Central Market (as suggested by previous posters)
5) The nearby Old Railway Station. Amazing Moorish architecture again
6) Grab a taxi and head off to the Petronas Towers but I'd skip the shopping mall inside because it's fairly generic.
7) Last, grab a cab and head off to the National Museum so you can understand the history. The musuem is not great and has a small collection (its maybe 2-3 floors and small as musems go) but in this case, it's perfect for someone in a rush: it'll give you a quick summary of the history of Malaysia from the Malacca sultanate, to the 3 colonial periods: Portuguese, Dutch and the English and the Independence, Emergency, The Split with Singapore and modern Malaysia.