I am a resident of KL. Yes, there are many half day and full day tour you can organize with the hotel which will also pick you from hotel. Some of the places you can move around on your own are as below all in the same area but you need a little of walking and the heat and humidity can be quite testing but its all part of tropical travel. You can make a loop of these places on your own in your own pace and they are in the same locations just few hundred metres of each others. Merdeka monument, Lake Garden, Butterfly Farm, Deer sanctuary, Bird Park (probably the biggest in the region with netted ara where birds flies freely - must visit). If you are staying in downtown KL, this place is just a few Ringgit from your hotel and get the hotel to arrange a taxi which charges by metre. Alternatively, if budget is not an issue, the preferred way would be to hire a chauffer driven care from the hotel to zip you around for a day which probably cost you a few hundred Ringgit, cost of a day's hotel stay.

I'm not sure about the tours but it's a good part of KL to visit independently. Many attractions are bases around the square including the City Gallery with an amazing model of KL, the cathedral of St Mary, the Sultan Abdul Samed building and apparently the tallest flagpole in the world! Some of the buildings are architecturally superb and one of them houses the national textile museum( if you visit there, we don't recommend the cafe in the museum!) I would avoid going around mid day due to the heat and if you are using one of the hop on hop off buses, it will stop at Merkeka Square. I can't include a website in my answer but there is a good one of Kuala Lumpur attractions.