re: Planning a first trip to Paris, is it bad to go solo?

Your time frame is a week, forget a day trip to Belgium. Be in Paris, don't run off to some place else.

Buy a multiday Paris museum pass...it will allow you to skip the ticket line most places. As for the Louvre...especially solo, it's a good idea to enjoy it in "bites" as opposed to staying in the place for 5 hrs straight. The entrance/security lines can be completely ridiculous, so plan to go early or at odd times. If you have the pass, you can pop in and out over a couple of days. It's open late at least one night a week.

I can recommend the Hotel St Paul Rive Gauche: small, family owned, within walking distance of the Jardin de Luxembourg RER station that will take you to & from the airport quite easily (even early AM). Not fancy, but pleasant, clean, and comfy. Minimal lobby, but coffee and breakfast are available at the hotel. LINK