You only get Fighters Guild contracts (quests) from three people:
the head of the Cheydinhal guild hall (Burz gro-Khash)
the head of the Anvil guild hall (Azzan)
and the second in command of Cyrodiil's guild, at the headquarters in Chorrol (Modryn Oreyn)
Those guys can also promote your character.
There are quite a few quests all over Cyrodiil (I count about 19) but you always get them from those three cities.
There are lots of misc quests and places to explore. Or you can start a new character. It actually doesn't make sense to me for a single character to do all quests. That seems to break role play. For example, why would a leader of the Dark Brotherhood want to do some low level quests for the Fighters Guild.