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You did not mention your budget.  The International Radius Hotel is in the heart of the city and quite reasonable.  It would be easy to get to KLCC on foot from there, mostly via the airconditioned walkway above the city. Otherwise try to find somewhere on the LRT rail line as the trains stop at KLCC.

Try airbnb [airbnb.com/] - haven't used in Malaysia before but hear it is good - usually can find good quality accommodation for reasonable prices.

If you are staying for more than a few weeks it might be useful to rent an apartment rather than a hotel (you'll get more space, sometimes a kitchen etc too)

Make sure near to Kelana Jaya LRT line if you want to go to KLCC a lot, that way no changing to a different line, which can add to your journey time

If you want to consider Maytower, it is 10 minutes walk to the nearest LRT station. You can take LRT to KLCC. If you are interested, do let me know. cheers...

Yap ..maybe u can try this .... I loved it.....

airbnb.com/rooms/2169054

In my opnion Jalan Scott in Bricksfield or Bukit Nanas or Titiwangsa area will be suitable for you. From bricksfield you can walk to KL sentral for Monorail, or LRT to KLCC same goes in for Titwangsa.

Or be in the heart of Bukit Bintang and KLCC by staying at Home Phoenix Guest House.