The most uncomfortable thing one can do is to question everything that is taken for granted and seek answer. Ask why/how you're able to access to internet, question why our society is like it is now, seek why you choose to be like you are. Try to see the other side of the norm. It is very difficult to imagine oneself leading a life doing these. But, it is also one thing you can do to improve your life.
On a daily basis, I try doing the following. It took a while before I realized that doing the uncomfortable things make me feel comfortable. Few of these are quite uncomfortable even as you read them. It just gotta be something that you thought to be good thing but burns a bit more willpower to take action.
Do one thing every morning that makes you uncomfortable, before having a breakfast. You can combine few things at once. For me, waking up before 6, quick exercise followed by a quick cold shower.
Reading a book 20 minutes before leaving home for university and immediately after reaching home.
Writing a diary regularly before going to bed.
Start talking to that girl standing alone in the bar looking at her mobile. Or, randomly giving compliments to the strangers on the street. Do it after initiating some random conversation, just to not scare them.
Adding value to conversations you have with everyone. Not just listening to them.
As per activities,
Go hitchhiking. Its hard first time. No, it feels like hard thing to do. But its not. You just gotta raise your thumb, on the road. Its scary, but makes you wonders. I got to meet wonderful people on the road, had best conversations that still comes to my mind sometimes.
Join an improv group in your city. Its scary as hell until you realize that everyone around you feels the same. I had inadvertently joined one improv group without knowing how challenging it would be, thought it would be fun. Didn't give up then.
Join a nearby toastmasters group, if you feel like improving communication skills. Its the closest thing you can do at your convenience.
Learn a musical instrument. At least start practicing and make a goal to give a public performance, however small it may be. Take lessons if needed. I once took DJ lessons and performed in a local night club for 20 minutes. Best feeling it was. Given how short I look, it was definitely challenging.
Volunteer for a non-profit organization or anything in principle so that you can a part of something big. I volunteered for TEDx. It was such an overwhelming feeling I had on the big day, being part of the community.