I just finished season 2. When the new season dropped in January, I was excited that it was back and dived into the first episode. I made it 15 minutes in before I became disinterested. Now, with a lot of extra time on my hands, I attempted the season again and am happy that I did. I thought everything really picked up after episode 1 and ended up enjoying the remaining episodes.
I think what made it hard for me to get into the new season was having Annie and the boyfriend go full steam ahead from the beginning of episode 1. As others have said upthread, he's an immature man-child, and for me, it really made me dislike Annie as well as lose interest in the show. I understand why she wanted to stay with him--he's her first real boyfriend, her low self-esteem inhibits her from realizing she's awesome and she can do better, etc--but it all made it difficult to root for her because I knew he was just going to disappoint her again somehow. Needless to say, I was cheering when she finally kicked him to the curb and I hope she doesn't take him back in the next season.
Things I really enjoyed about season 2: pretty much everything outside of Annie and the boyfriend. Fran was once again the best character, and her tall friend whose name I didn't catch was great as well. I would totally be best friends with both of them if they were real. I hope they are still a thing next season. I also liked Fran's family stuff. If it was mentioned before that she is Nigerian, I didn't remember, so the Nigerian wedding storyline was an interesting surprise. I have American friends whose parents emigrated from Nigeria, so the wedding and all the family dynamics felt very real to me. I also liked seeing Ego Nwodim outside of SNL and thought she did a great job as Fran's cousin.