You have two posts open with the same title and info. I have also posted in that one. This is what I said:
Hi frequentTraveller, you ask many questions that really can't be answered. Paris is covered in metro lines and there are so many metro stations. I think you should start looking at a guidebook to get the layout of the city and see where all the musuems, gardens, and other sites are. Regardless of which hotel you decide on you will never be close to all attractions.
Also, you don't want to spend over 250 what a night? Euro, pound, CA$, AU$, US$? You need to specify and should specify in Euro as that is what a hotel will charge you in.
On Trip Advisor alone there is over 1800 hotels rated and over 9200 restaurants rated. They are possibly all close the metro, but which one?!
Also in 4 days (do you mean 4 nights, in which case you will have 3 full days) you won't see it all. You really really need a good guidebook to get you started and then we can help you once you have more of a plan.
Edited: 9:30 pm, April 11, 2013