He seems to be limited to the near past
As far as we've seen, without the Three-eyed Raven, Bran has been able to Warg as he wants, but has never mentioned anything further back than Lyanna's wedding (if I remember correctly). However with the fully "trained" Three-eyed Raven, they were able to go all the way back to the Age of Heroes (to witness the creation of the first White Walker).
One thing that we need to notice is the more recent ones Bran has done without the presence of a Weirwood right next to him. The travels with the Three-eyed raven, and others on his way south, always took place next to a Weirwood. It would seem in the show canon, up until late in season 7, he wasn't shown being able do any form of greensight/time travel without a Weirwood. This trend is broken when he is sat in his room and sees the wedding between Lyanna and Rhaegar after Sam mentions it.
Another "missing Weirwood" is in the memories he's visiting. At the Tower of Joy, although Bran might be by a Weirwood in the present, there's no distinct Weirwoods in the Tower of Joy scene and I believe in the book canon there are no Weirwood trees that far south (in Dorne). Furthermore, in the Throne Room, there is again no Weirwood, yet Bran was able to witness Petyr talk about ladders and their chaos.
In conclusion, it seems at the height of his power, the Three-eyed Raven is unlimited by how far he can travel back, however as far as we know requires a Weirwood to see the distant past, both in the present and in the past. The nearer past Bran seems to be able to see regardless of proximity to a Weirwood (such as Petyr's scheming and the Tower of Joy scenes).