I'll arrive in Paris at 8am and I'll spend the day over there. I will be on foot. I need to be in Brussels City Center the same day before 9pm [Hotel]. What is the quickest and reasonably cheapest way to go from Paris to Brussels? I saw that the trains [Thalys] leave from Paris Nord, but that's a 1h walk from the Arc de Triomphe. Is there a Bus/Train I can get close to the tourist places such as Eiffel Tower and Arc de Triomphe?
Nothing is going to beat Thalys time-wise and Paris-Nord isn't too far away from the center as far as long-distance “departure points” (whether airports, train stations or bus terminals) go. You simply need to combine Thalys with a subway, RER or taxi ride from wherever you find yourself.
Even if you could find a bus starting closer to your actual point of departure, it's going to be much slower. Trains other than the Thalys will also leave from somewhere else and/or require several connections or a long travel time. Both solutions could be considerably cheaper, however.
Ridesharing could also be a way to save some money and leave directly from another part of the city than the train station but it requires a lot of flexibility and would not be very fast either so it probably does not meet your requirements.
Also, among the main central sights, the Arc de Triomphe and Champs de Mars are already a bit away from the very center of Paris. You could plan your sightseeing to start there in the morning and end up near Châtelet/Les Halles, Saint-Michel – Notre-Dame, Cité (close to the île de la Cité, the Louvres or the Tuileries) or another station on subway line 4 or RER line B or D. Same thing if you intend to see the Grands Boulevards, Montmartre or the Opéra area; go there last, not before seeing the Champs-Élysées or the 1st arrondissement.
City to city buses are considerably cheaper than trains (you can often get tickets for as low as €9 when booking in advance), but the fastest bus trip takes 3:50 vs. just 1:20 on Thalys trains. The train is definitely fastest even though the station is less convenient to the sites you mentioned.
If the much longer travel time is worth savings and convenience to you, there are a few bus companies which you can compare on Busbud (full disclosure: I work on this project). Some buses leave from Porte Malliot (10 minute walk from Arc de Triumph) and some leave from Bercy (5 minutes by metro from Châtelet which is close to the true center and sights like Notre Dame).