"Rhûn" just means "east", so it's more-or-less equivalent to saying "over thataway".
Tolkien never mapped nor fully described the region, but we do know some of what's out there. In the original symmetric design there was a range of mountains to the east, mirroring the Blue Mountains in the west; the Red Mountains (Orocarni), and it may be surmised that these are still there (the west recieved far more damage at the end of the First and Second Ages; the east appears to have been relatively unscathed).
The Mountains of the Wind were towards the east and slightly south too. According to a
wiki page they were destroyed in the War of Wrath, but the only evidence I can find that they may no longer exist is the fact that they appear on Ambarkanta map IV but not on map V (and map V still has Beleriand on it so it pre-dates the War of Wrath, meaning that if they were destroyed it was before then).
The Inland Sea of Helcar existed in the east too; according to one theory it shrank (possibly draining into the Bay of Belfalas/Great Gulf) at the end of the First Age, leaving behind Mordor (which by this theory would have been underwater in the First Age!) and the Sea of Rhûn as a remnant. This seems to be based on not much more than a speculation by CT in one of the HoME books (and an attempt to match Ambarkanta map V with the later geography).
However, the Cirdan essay in HoME 12 states that the Teleri lived by the Sea of Rhûn for an extended time during the Great Journey, which seems to me to indicate that they're separate seas.
Beyond that there's a shore, the east sea (narrower than Belegaer) and an eastern continent mirroring Aman.