I lived in KL for 14 years (back in the UK since June)
It's pretty safe as long as you are sensible. Decent length shorts and T-shirts with sleeves. You will see tourists in vest tops etc, but I wouldn;t advise it. Take a shawl/wrap in case you need to cover your head.
Download the Grab app for taxis and Ubers, all trackable, very safe. The new MRT is ok for getting around too.
The Airport is a fair way out of town, so you will need to budget for the train into the city - KUL- KL Sentral is about 10-15 pounds a day I think.
My favouirte places to take visitors was the KL Tower (on a clear day for good views), the Petronas towers (visits to the Sky Bridge can be pre-booked), the lake gardens - which includes the Bird Park, butterfly Garden and Orchid gardens - probably two days worth.
For local street food, you can't beat Jalan Alor.
China town and Central Market for touristy shopping, very safe but watch your bag. Haggle on prices. Close to the National Mosque - very tourist friendly but wear long trousers and sleeves and take something to cover your head.
Thean Hou Chinese temple well worth a visit (Short taxi ride from KL Sentral)
If you fancy a day trip out - the Elephant Sanctuary at Kuala Gandah. It would take a whole day if you do Batu Caves on the way. There are organised tours you can book for this.
You can also do Melaka as a day trip, old Dutch town, lots of Junk/Antique shops, excellent food (would also be a decent weekend trip with DH)
There is no real monsoon season, just wet days and dry days. Don't worry about the rain, if you get caught in it, you'll dry off.