Is it normal to stray from your partner?

I recently graduated college/moved to the big city. Met an awesome guy within a month of moving here. He's 29, im 23. Things were almost too good to be true with us at first; he and I constantly laughed together- Crazy about each other. Then we started really getting to know each other... He is very moody/mopey (to my surprise), and never wants to do anything but smoke pot and watch tv/sleep. I want to go meet people, do things, experience stuff.. I have a zest for life and he never wants to take me out/go on adventures together. Everything I suggest/say gets shot down and he never cares to listen to what I want. It's not hard to make me happy. Take me out once in a while! We have been fighting a lot, but we love each other and always make up. Our 6 month is tomorrow, and Valentines Day is Saturday. He actually made an effort to plan these days out for activities for us to do. He was changing for the better.. But unfortunately I made a mistake and cheated on him when I went out last week. I met up with a "friend" of his at the bar who told me that he is a selfish and difficult person. I think she may be right, but what kind of friend would say that? I met a random guy after who cheered me up, and we ended up fucking. I felt like total scum and thought my bf deserved to know, so I told him right after. Its been a rough few days, and he said he needs a few weeks to figure this out and that he still loves me. I did what I did because Ive felt neglected, and it was a selfish act on my part. But are we just too different? It's up to him now. I'm taking a vacation next week to do a cross-country trip solo and try to find myself. Is it normal to stray, and are these issues in our relationship "normal"?