I just need to go home first and then I'll join you.
どちらも、「まず家に帰らないと。それから行くね」というフレーズです。
「あなたが飲んでいる場所に行く」なら、I'll go to the place where you're drinking などと言えます。
... first and then ～というパターンは、「まず…してから、～」と言うときの定番表現です。
I'm gonna pop back home first so I'll see you there.
★ポイント：①ちょっと家に寄っていく感じ→I'm gonna pop back home first
pop:ぴょん、という感じです。
②（だから一緒にその場所にはいかないで）現地で会おうね→I'll see you there.
I'm gonna pop back home first so I'll see you there.
英語職人☺
I'll hang out with you, but I need to go home first.
I need to make a quick stop at home, but I will catch up with you later.
Use words like "after", "first" or "later"when talking about doing things in a particular order. The sentence can be in chronological order or not depending on how you choose to say it. Use "but" to connect the two parts. "but" in this sense means however.
I'll be with you shortly but have to stop off home first.
When invited to hang out after work., and you want to say that you will go home first and then go hang out with them, then using either of the above suggestions should express that pretty well.
I need to stop by my house first and then I'll meet you there.
If you "stop by" somewhere, it means that you will quickly visit it. It's important to tell your friends that you will see or meet them later so that they understand that you will be hanging out with them. I hope that this helps. :)
日本 
アメリカ合衆国 
イギリス 
