Who could be an "important" hobbit in Esagorth?
(Someone that could give Rewards to an hobbit character)

What about Mungo Butterchurn, cook and proprietor of the ' Comfy Chair' inn. He arrived in Laketown the previous year in the company of a Dwarf named Bori. This Bori claimed to be the youngest brother of no less than three of the Dwarf's of Thorin Oakenshield's company.
Bori continued on to Erebor but Mungo decided to take up residence. He has a wealth of wild tales, from caverns filled with gold and goblins in the misty mountains to foggy moors in far off Eriador where the the bones of ancient Kings rest anything but easily. Whatever the truth of these tales he certainly had come across enough gold to purchase his own inn at the edge of Market square.

I was thinking about a "famous" hobbit (i.e. named in one of the books), but this is good too :-)

There are no canonical ones... However, you could easily write one in. for example, the tooks had a bad reputation for going off on adventures. It would not be a huge stretch to say one had set up in lake town or dale

By a happy coincidence, it just so happens that Mungo is a Took on his mother 's side. His mother is Marigold Took of Long Cleeve and thus he is directly descended from Brandobas 'Bullroarer' Took.

I think it would be more appropriate to receive a gift from Bard or one of the dwarves or King Thranduil (or Legolas). Hobbits are a long way from home, and the ones in the books always get their "stuff" from other races.

Yeah, I probably agree with that last post by Voidstate. It depends on how much of a stickler the LM is for the gift matching it's description in the blurb.
Quick question, Patrons don't have to be canonical, do they?

Yes, but it's difficult to have a cultural specific reward from a member of another culture.