I don't feel like going to that cafe because people can smoke there.
I don't want to go to that coffee shop because they allow smoking inside.
この場合、次のような言い方ができますよ。
ーI don't feel like going to that cafe because people can smoke there.
「あのカフェは喫煙ができるから行く気がしない」
ーI don't want to go to that coffee shop because they allow smoking inside.
「あのカフェは中でタバコが吸えるから行きたくない」
ご参考まで！
I don't want to go to that cafe because people can smoke there.
"あそこのカフェは喫煙出来るから行きたくない。"
I don’t wanna go to the cafe because people can smoke
-> I don't want to go to that cafe because people can smoke there.
"wanna" は話し言葉です。カジュアルな会話メッセージを送っているときなら普通ですが、正しい言い方は "want to" になります。
他：
- That cafe allows smoking so I don't want to go there.
カナダ 
アメリカ合衆国 
