You could walk between the Eiffel Tower and the Louvre (3 km = under 2 miles) or take the métro or bus. Check the http://www.ratp.fr website to download maps and other info. How long it takes to cover the whole of Paris depends on your idea of sightseeing. 2 days is a bare minimum to get a glimpse of the main attractions. But you could stay weeks and not have time to enjoy everything either.

No need to take tours unless maybe those bicycle tours, they are kinda fun and you learn a lot. A less sporty way of seeing the main attraction is the boat tours on the Seine. If you are traveling alone and haven't prepared your trip much hiring a tour guide for yourself can be a good idea for half a day or so, otherwise forget it. Your hotels will have brochures or you can get a list or tour guides from the tourist office (www.parisinfo.com). Don't go on any of the big tours, they are ridiculous and a complete waste of time.

Having said all this, before even looking at properties near Paris, you should investigate if you can move to France where immigration laws are now those of the Schengen zone. Basically any person from a country outside the Schengen zone is not allowed to move there for a period exceeding 90 days unless they have been granted a long stay visa. They must also obtain a work permit and a living permit. These are now rarely given, unless you have outstanding qualifications or have been offered a job there by an organisation that can justify not employing someone from the EU, for instance working at the American embassy, or teaching a very specialised subject in a university.
You can check all the information about living and working in France on the following website:
http://www.diplomatie.gouv.fr/en/espaces_dedies.php3?id_rubrique=2045

Paris in general is a very safe city, but like anywhere else in the world, keep your wits around you and be aware of your environment. Don't go wandering someplace that you're unfamiliar with when it's dark and there's very little people around. Don't flash your belongings to the world and take good care that your belongings are securely kept. Don't drink/eat something offered by a stranger. If you're out for the evening don't let your drinks be out of your sight or else just buy a new one. The usual things and precautions that you would take regardless where you are, you know.

Walking the city in the central area is very much the thing to do (you'll miss the magnificent sights of Paris with the lights otherwise) during the evening, but you may want to avoid areas such Pigalle (red district area) and Montmartre, and parts of the city that's near the peripherique.

Stay safe and have fun in Paris.