Access to the outer planes (and vice versa) became nearly impossible after the fall of Un Talan Vi. The deities used to travel back and forth even if such travel was somewhat infrequent. Tyar was never easy to find even when one knew where to look.
It is theorized to be easier to get to the outer planes from Tyar than it is to reach Tyar from the outer planes. People sometimes leave for the outer planes, and what signs we can read suggest they might reach their destinations. Experiments where someone or something were supposed to return from the outer planes have failed up to this point. All scholars really know is that the timing of increased difficulty in travel between Tyar and the outer planes coincides with the fall of Un Talan Vi.
The Ethereal plane is accessible from Tyar. The path to the Ethereal is a strong river whose current flows away from Tyar in the direction of the Ethereal. Returning from the Ethereal is a trial unto itself. Travelers from Tyar may pass through the Ethereal to reach other planes, but must sever any personal connections with Tyar in order to do so. The tether to Tyar will not reach through the Ethereal into other planes. As far as anyone knows, it is impossible for someone to travel to Tyar through the Ethereal without a personal connection to Tyar.
Denizens of Tyar may travel into the Astral plane with no greater effort than that required on most material planes. Those with personal ties to Tyar must sever their personal ties with Tyar before they can leave the Astral plane unless traveling to Tyar from the Astral plane. The traveler has to essentially commit a sort of suicide if she wishes to reach a different plane and has a personal connection to Tyar. It is possible for somebody without a personal connection with Tyar to travel to Tyar through the Astral plane, but it is and arduous task to do so.
The elemental planes are accessible. It is difficult to find Tyar through the elemental planes, but it is possible. Like with most planes, having a personal connection to Tyar increases the chance of being able to travel to Tyar tremendously.
Tyar does not have any direct connection to the Feywild whatsoever. Even the seemingly wild tears that sometimes form to other planes have yet to produce any reports of openings to the Feywild. Fey and Eladrin are practically unheard of for this reason. Some may have traveled to Tyar via other routes, but never directly through the Feywild. Scholars most likely do not realize the Feywild exist, or if they have heard accounts may believe it to be another material plane.
There was no connection to the Shadowfell until the imprisonment of Nylva. Shadar-Kai are considered the new kids on Tyar for this reason. Since Nylva is thought to reside in the Shadowfell it is likely she would have an easier time physically entering Tyar than other deities at this time. Some scholars believe Nylva is the Shadowfell which would explain why she has not returned as of yet. Those without a personal connection to Tyar find traveling through the Shadowfell to Tyar to be somewhat arduous, but it is doable.
There are lots of small roving openings to other planes. The Wandering Border is full of such portals. Most of these open to material planes, elemental planes, and the Shadowfell. A few open up to the Far Realms It is difficult for deities and the truly powerful to use these portals to get onto Tyar as they are unstable and prone to collapse. Travel to other realms from Tyar using these portals is typically easier. They seem to break down faster when something travels to Tyar than away from Tyar.
The Far Realm is just as accessible from Tyar as from any other material plane. Unlike most planes, the reverse holds true as well. Tyar does not actively push against travel from the Far Realm. This might be the fastest path to reach Tyar from the outer planes, but is wrought with madness and one would still need to locate Tyar.