1. The chosson does not recite tachanun during the seven festive days. Any minyan where the chosson is present does not recite tachanun. (Shulchan Aruch 131:4 and Mishnah Berurah)
2. If the chosson left the synagogue before tachanun the poskim disagree as to whether tachanun is recited. (Ishei Yisroel page 268)
3. If the chosson is not in the Synagogue but the kallah is in the women’s section, tachanun is still recited. (Yaskil Avdi 7 Hashmatos 3 and Shevet Halevi 5:12)
4. The Maharsham (Daas Torah 131:4) writes that even if the chosson is not praying with the minyan, his mere presence warrants the omission of tachanun. However, the Aishal Avraham of Botchetch writes that if the chosson is in the Synagogue but is not praying with the minyan, tachanun should be recited. It is preferable, however, for him to avoid this question by leaving before tachanun. This is also the view of Rav Ovadia Hadaya zt”l. Harav Shlomo Zalman Auerbach zt”l says that if the chosson enters a synagogue not intending to stay long and he happens to be present when the congregation is about to pray tachanun, then tachanun should be recited. If, however, the chosson intends to stay in the synagogue, even if he is not praying with the minyan, tachanun is omitted. (Shalmei Simcha page 139)
5. If there is a “break away minyan” outside of the main synagogue and there is a chosson praying in the main synagogue, the poskim discuss whether tachanun is recited in the “break away minyan.” They conclude that if the “break away minyan” has its own aron kodesh and bima, it is then considered it’s own synagogue and they would recite tachanun. If, however it does not have an aron kodesh and bima, it is considered an extension of the main synagogue and this minyan is also freed from the obligation to recite tachanun. (See Shulchan Haezer vol. 2 page 119)
6. The Taz writes that it is better for the chosson to pray on his own this week, then to pray with a minyan because his attendance will cause the omission of tachanun. The Sefer Toras Chaim strongly questions this ruling. He cites many poskim who say that if the chosson steps out of the Synagogue before tachanun, then the tzibbur does not omit tachanun. Therefore, argues the Toras Chaim, the chosson can attend the minyan and just step out before the tachanun prayer is recited. This way he will be able to pray with a minyan. (We have seen that it is indeed an argument among the poskim whether tachanun is recited if the chosson left the synagogue (Halacha 2) before tachanun. Perhaps this is the area of contention between the Toras Chaim and the Taz.) The Sefer Shulchan Haezer rules in accordance with the Taz. He adds that the chosson should preferably gather a minyan together in his home.