Unfortunately, I do not stay near KL city center, but if you also travel by LRT train from one spot to another, there is one Costa Coffee at Nu Sentral. You may take LRT train to KL Sentral station, Nu Sentral is just there.
P/S: I am not good in guiding as I do not grow up at KL.
Have a grest my travel and fun time. Bukit Bintang itself is already a happening place, and many other nice coffee shops to explore 😉
Thank you so much for those useful info! It's going to be my 2nd time in KL and I am going to stay longer like a week or two hehe