Hi lindoro! I'm so excited for you!
The only problem with wonderful, big cities like Paris, is that they've become so commercialized, it's hard to find a quiet, understated spot to just kick and relax, sipping on something refreshing, without being disturbed, as a novice visitor.
But don't rule out some of the major sites, b/c you could still go to one that is quieter and still relax and see something. You could go just to sit and relax and come back later when you're rested to really see the place again.
This is what I'd recommend:
When you arrive in the morning, take the subway to your hostel (note: don't buy the multi-day cards, it's not worthy it, it's cheaper to pay your fares individually as a lot of places are walkable, etc., but you decided, check it out carefully first). Ask for a metro map.
Go to your hostel and drop your backpack, even though it's lockout, you can still go in and drop it off, you're just not allowed to remain.
At this point, go get something to eat. The cheapest way is to spot a crepe vendor off the street or little shops. In addition to sweet crepes, you can get ones w/ cheese, lettuce, tomatoes, meats, they are huge and oh so cheap.
You can also spot any patisserie or brasserie and eat something. Brasseries are like you upscale french version of american diners. You can eat and relax, so long as you find a less busy one. But lunch time, they do tend to be packed. Next time I'm there I'll want to visit the famour Cafe Flore which has inspired the minds of so many left wing artists, philosophers and politicians. Another less expensive choice, is to find a supermarket or grocery, but then you'll have to eat in the street or park.
Depending on the weather, and I assume that it will still be a bit chilly when you get there, so sitting outside anywhere for a prolongued period of time might not be an option, so I'll take you indoors. Try the Notredame Cathedral or Louvre/Musee D'Orsay/Picasso museums, even though these are major sites, they will offer you places to sit, rest, and relax your eyes on a pleasing site. You can come back later and revisit them, but this time, sit back and relax. The Louvre might be good, since it's so big, even if you see something on your first day, there will be lots of more stuff to see when you go back to really tour the place.
Once you've eaten and are more relaxed/rested, slowly track back to the hostel by taking in the city sites. Walk by the Seine river, anywhere from the Arch de Triumph through the Place de Concorde (near the Louvre), etc... Sit along the way, rest and continue...
Go to hostel, check in, shower if you want, lie down a bit, take a nap, at night, meet some folks at the hostel, and head out to Latin Quarter, Marais, Montmartre, there's another area near one of the 2 major opera houses, I forget the name, that has an alternative feel to it..., or Montparnasse (eateries) and enjoy!
Hope this helps.