Going on your own to a new place can be really frightening, but means also freedom and endless possibilities. In those 25 days off work in a year, i want to do things i like and really make the most of it. That doesn't mean that you can't have an amazing time with friends, but it is always very hard to find the right travel buddy.
So if you decide to go on your own, it's nice to have some perspective and it's quite fun to not care, what somebody else would like to do (that sounds selfish, but this vacation is about you and your dreams!)
In order to feel safe and comfy by your own there are some basic things you can do.

Collect as much information as possible about the place you are going to. Whether it is about culture, politics, religion and also distances. I did not know Bali was as big, as it was until i finally went there. So some stuff i planned to do, was literally impossible because i did not look at the map scale properly.
Also consider different living standards and health care in other countries. I was especially scared of tropical diseases, like Malaria, and more likely Dengue Fever and Stomach flues. For mosquitos i can really recommend Repel100 spray. In two weeks i got bitten only once!
In addition to avoid having a bad time from the totally different food bacteria, one can take a cholera vaccination as well. I might have been a bit overreacting, but i wanted to be as safe as possible!
So after taking care of these more general things, the real fun part can begin: to plan your activities!
After choosing Ubud and Gili Air as my main spots to stay, i borrowed some travel guides from the library,which seems quite oldschool, "lonelyplanet" is my favourite, but the biggest sights to see, will never change. One can also find really nice advises on Tripadvisor.com.
So i made a list (again) with all the places, that i was really interested in and that were absolute obligatory to see.
Take in consideration how long it takes to get there, and which places might be close to each other, so you can do them the same day. The best way to find some routes and daytrips is actually with google maps. You just type in your destination and your place to start, very often there are spots just shortly away from the route, that might be super interesting as well, but are not mentioned on big travel sides.
So if you have picked your main destinations and enriched them with some little nice spots around, you can decide what to do on which day. Also important for museums or temples: look up opening times as well, so you don't plan stuff on the wrong day. Sometimes you can just change one planned day to another, but if you rely on a scooter or driver, booked for a specific day, it is not that easy to change spontaniously.
If you have your days planned and full with activities, you can't get bored and start thinking about being lonely. To not get stressed out too much, plan some extra time every day, because you might want to look a bit longer at some place. Also it is very nice to just plan some spare times for literally doing nothing and just explore or wander around, you might be suprised what you can hit. I always plan in a free afternoons every third day, so in case something goes wrong or takes longer, you still are able to fill stuff in that empty time.
Planning and preparing is really good, but don't panick, if things don't turn out as you thought. As mentioned before, i planned to drive to almost every temple by myself with a scooter (because it looked all so easy on the map), but when i was on Bali, i decided to book a driver instead, which saved a lot of time for me, so i could do other things that were not planned.
How much you plan and in which way is up to you, but i consider being over(prepared) as a really good sign. You always have some backup possibilities and that is a great security.