First of all, there needs to be a reason for Nicea to focus on the East and a reason for them to not recover Byzantium. This can be done by a Bulgarian capture of Constantinople before the 1240s. This Bulgarian empire would in many ways adopt Byzantine customs but continue to use Bulgarian as the military language and would speak Greek for prestige. The empire would also encompass the Despot of Epirus this killing all successors of Byzantium save Nicea. With a massive Bulgarian empire in Greece, Nicea looks eastward toward Trebizond perhaps.
Nicea if centered in Anatolia will have a better time against the Turks then if they were in Greece. The Seljuk sultanate of Rum is quite strong and will not be easy to invade. However time is on the side of Nicea, as the Mongol horde comes in and curb stomps the Seljuks in 1242. This gives Nicea the opportunity to take the central of Anatolia, perhaps immigrating crowded Greek settlements eastward pushing the Turks back. The Turks might leave before then though if Nicea attacks right after the Mongol horde, then it might be enough of a shock for the semi sedentary Turks, and they precede to migrate elsewhere (perhaps toward Caucasia). Nicea will then set its sites on Trebizond, who it will not be impressed with and will take the fragile state, perhaps with Trebizond surviving in Kaffa and such in Bosporus. To stay powerful, I would suggest for them to create an alliance with the Ilkhanate against the Niceans biggest threat, the Mamluk sultanate of Egypt led by Saif ad din-Qutuz, to make things safer have Qutuz after defeating Hulagu survive Baibars coup attempt and kill Baibars for treason. This gives Outremor some breathing room who will probably become a buffer zone between Nicea and The Mamluks.
However the biggest threat in the future is the rise of Timur and the near inevitable fall of the Ilkhanate (which would need tweaks to be saved). Once fallen, Nicea will be on its own for the most part, and will have to go toe to toe with the Timurids (not fun) they will meet the same (or worse) fate as the Ottomans did under Bayezid. What to do afterwards is up to you, however I will post more on future later as I get feedback.