Many people who consider themselves "people persons," allow their need for human interaction to hinder their chances of having fun experiences and often think that it's impossible to have fun by yourself... but on the contrary, you can have a ton of fun by yourself.
1. Be comfortable with who you are first.
The number one thing, before you can be self-reliant and be content with having a good time on your own, is being able to accept yourself for it. Don't think of being alone sometimes as a bad thing, and be able to cut the ties from social interaction to be able to do things by yourself without the social support of others. You don't need your friends to be by your side all day every day. Friends are great to have in life, but their presence doesn't define who you are. You're still your own person.
2. Take a stroll when nobody is around.
Once I went skateboarding at 5:30 in the morning on New Year's Day and there was literally no one outside and watched the sunrise. It was the greatest sense of freedom I've ever had. So hopefully you can find something like that if you choose to go out early in the morning before everyone wakes up for a nice stroll or jog around town by yourself. It'll really make you feel at peace with everything and is a great stress reliever. (except I wouldn't recommend going out at night because that's scary)
3. Go to the gym alone.
Workout out by yourself can be a great self-motivator because when you go to the gym alone, you are the only one that can motivate yourself to do all the workouts that you set to do and push yourself to the next level. It's also great for getting your brain to be more focused on the task at hand, without the distraction of another person being there.
4. Eat alone.
Go out to a nice restaurant in the city, sit outside and watch the cars go by in the glare of the moonlight on a nice Saturday evening...or just go to the dining hall. Either way is fine, whichever you prefer. Eating alone may seem pretty boring to most everybody, but its all in what you put into it. Just go ahead and people watch. Consider it your downtime to recollect your mind and your thoughts and use it to de-stress everything. It's not as bad as some people make it out to be. (also no one is gonna watch you eat or see what you choose to eat if your self-conscious about that sort of thing, which some people are...there's no judging unless you judge yourself)
5. Be more positive.
Should've said this earlier, but the key to having fun being alone is about keeping a positive mindset through all of this. If you're able to say to yourself that you will keep an open-mindset about things and try to have fun then you will. It's all about trying in this scenario. Two people can go do something by themselves and one will leave unhappy and one will leave happy because of the mental choices they made. If you continue telling yourself that you "wish your friends were here" or anything like that then you're missing the point. You have to live more in the moment, then you'll be happy and content with life on your own.