Albania has been a member of NATO since 2009, and (just this year) has begun negotiations to join the EU.
Not every "Western" country is a NATO member, but NATO members are usually counted as "Western". Similarly, EU member states generally count as "Western", and a country formally negotiating to join the EU probably falls in that bucket too.
Turkey is possibly the big exception to the generalisations that "NATO member"="Western" and "negotiating to join the EU"="Western". However, Turkey used to have much more of a pro-Western orientation when it was ruled for decades by secular nationalists. It is only in the last 20 or so years, with Turkey being ruled by the religiously conservative AKP, that Turkey has been moving away from a "Western" identity. But Albania's politics are very different from those of Turkey. Albania's politics are dominated by secular parties. While both Turkey and Albania are majority Muslim, the kind of religious conservatism which is the driving force behind the current Turkish government is far less popular among Albanians.