its going to depend on how delivery goes, with my first baby I had 17 stitches and took me a few months to begin running again. With my 3rd I had 1 stitch (she was small) and I began running 3 weeks post partum, however a small hernia prevented me from lifting again a bit longer. Listen to your body and talk to your doc!
I don't see any reason to think you cannot begin walking when you feel up to it...... I took my little girl on a hike when she was a week old

I started doing very slow walks about 2 weeks pp (only down one street and back) and as I gained strength gradually increased my walks but still at an easy pace....giving birth takes a lot out of you and you will probably not be physically able to do an elliptical until 6 weeks pp...I had a lot of stitches (not sure how many because I was afraid to ask, but I had one of the worst tears you could have) but I was still able to start jogging at about 5 weeks pp....just take it easy and listen to your body (and your doctor)...even after you have been cleared you still may feel like you need to wait a little while...even though I jogged through 32 weeks and took long walks/did light cardio up until delivery, labor/delivery took a lot out of me....your bladder control may not be the same at first and take that as a cue that you are doing too much...little by little you will get there and trust me it IS possible to work out like before, but you have to give your body time to heal...I would say that by 4 months pp I was back to doing intense cardio/longer runs and felt like normal. Now at 6 months pp I feel great!

As I understand it, even if you have a seamlessly smooth, perfect birth you should wait at least 2 weeks before doing anything. Walking would be fine at that point, I would still pit of the elliptical until 6 weeks.
Don't sweep or vacuum though. Look it up if you don't believe me. It is hard on the uterus that is trying to go back in place if you are raking/sweeping/vacuuming - anything with that push/pull motion.