I need suggestions as to where to stay in Paris so no car is needed for a 4 day "try to see the highlights of Paris" self tour.
A car is rarely, if ever, needed in Paris. It has excellent public transportation. If you type Hotels in Paris into the search box at the top of the page you will find many threads with hotel recommendations. If you look at a map of Paris, you'll see that the 1st-7th arrondissements are nearest the Seine, in the central part of Paris. You can't go wrong by choosing a hotel in these areas, close to a Metro stop. I like staying close to Notre Dame, in the Latin Quarter. Others like le Marais and Ile St Louis.
Try to stay near a METRO stop. With some pre-planning at home, you can work out quite an itinerary and won't need a car. The Hotel Eiffel Seine is one such spot - across the street from the station Bir-Hakeim. That is above-ground but offers access (with some changes) to the Eiffel Tower, Arc de Triomphe, etc. Hotel Web Site
Another good choice is the Hotel Muguet which is around the corner from the Ecole Militaire metro station.Hotel Muguet
I have stayed in both and found them to be clean, friendly staff and close to all major sites, shops and restaurants.
Again, by using the on-line site for the Paris Metro (Paris Metro Site) I was able to pre-plan my activities and move about quite easily.
Your question makes Europeans laugh: a car is totally useless in Paris, as in most European cities.
You can stay virtually everywhere in the city centre and find yourself a few minutes' walk from the nearest metro station.
Make sure you know where you are parking this useless metal box. Hotels are unlikely to have parking (and if they do you pay), on-street parking is virtually non-existent and you will have to pay for parking in a multi-storey car park some distance from your hotel.
Anywhere in Paris city will have a métro station nearby.