I am a fairly frequent visitor to Paris. My number one place to visit is the Musee d'Orsay. The Louvre is huge and busy so it is difficult to see the key items and is more tick the boxes. Musee d'Orsay is all impressionists huge collection of Monets, Manets, and Degas along with many others much less busy and more compact. Next on my visit list is the Sacre Coure, I much prefer the view from here than from the top of the Effiel Tower and you walk round the corner to Monmatre. Versailles is lovely, but busy. Pre-book on line for an early slot it is worth getting there before 10( the tour buses arrive then).
We went this summer for a long weekend. Stayed at hotel recamier which is on a lovely square ( Saint Sulpice) and the staff were all wonderful. The square has a fountain which is lit in the evening and we could see the Eiffel tower in the distance from our balcony (lights up with sparkly lights on the hour for 5 mins once it is dark)from our higher floor room. Had the most luxurious category of room, not cheap but so worth it. Very near the Luxembourg gardens which you should definitely visit and St Germain which is such a pretty area and great for cafes and people watching, window (and actual) shopping. Herme patisserie is on the opposite corner of the square Ladurre just a short distance away.
When I have been to Paris previously it was on a budget and I didn't stay central and to be honest didn't like it that much. Too much metro. This time I had a wonderful weekend. We did lots of walking, so make sure your shoes are comfortable. Liked the hop on/off batobus on the Seine and otherwise did walking and taxis when we got tired,which were very reasonable in price. Musee d'Orsay would be my preference to the Louvre if I just had a weekend as Louvre just so big and crowded. I would get to either of these well before opening time at a weekend to join the queue and plan what you want to see and not spend too long in the crowds.
We had a drink this time in Cafe Marly early evening instead of going into the Louvre,after a walk through the Tuileries gardens to the l'Orangerie small museumto see Monet's waterlilies and the Place de la Concorde, which is next to it. There is the temptation to do too much, so I would plan a couple of things each day. We got up early, although it was so tempting to lie in, and did a couple of sites before 10am,as certain places such as Notre Dame open at 8am, so you don't have to queue at all and see them without any crowds. Then take time to sit and relax in a cafe.
If you really want to go up the eiffel tower book online at the release date(see the site as soon as the tickets are released or you will queue - for a long time.... We went up again this time because of children pressure (who loved it) and the view is great,but it is pickpocket/sign my petition central because of all the tourists. Didn't really have any issues anywhere else. I'm not keen on Monmatre,so didn't visit this time. We went to les Invalides ( which we enjoyed - lots of war history but the kids found too much)and then through the gardens and across the Pont Alexandere III to catch the batobus back to St Germain this visit. Wouldn't do Versailles,although it is worth visiting,if you only have a long weekend as there is so much to see in central Paris in a short space of time.
Our best bits were just sitting in a cafe or the Luxembourg gardens on the Sunday, soaking up just being in Paris. Planning to see too much doesn't work as you just feel hassled by the other tourist crowds and tired of walking! I wouldn't bother with 1st class eurostar unless the difference in price to standard class is very small,but spend the money on a good central hotel instead.