Got online tickets from the official website to Eiffel Tower at 11:00 am

Tons, but if you are looking for something close by, The Invalides with the French Army Museum and Napoleon's Tomb is about a 15 minute walk from the Tower. You might also want to be there a few minutes before your appointed time. At 11, they will start allowing people with properly timed tickets to board the elevator, but there will still be a line of people because only so many people fit on the elevator at one time. There will be some waiting, especially you arrive just at 11.

That's right Sam, I want something near.

Musee Rodin outdoor sculpture garden, The Thinker, etc is nearby.
Take a look Seine cruise on Bateau Mouches, dock is directly across the river from the Eiffel Tower.

Its Bateaux Parisiens that is by the Eiffel Tower. Bateau Mouches is on the right bank a little up river, not there is all that much difference between the two.

Get to the tower at least 45 minutes ahead of your timed ticket. There is a security line that you need to get through before you get on the 'grounds' of the tower and line-ups are long.

Which company is better for the Seine cruise?

I don't think there is a dimes worth of difference between the two already mentioned biggies. Same routes, but Bateaux Parisiens is right there by the Tower on the same side of the river.