I started playing about three weeks ago and was totally lost. I am now 31kly away from the bubble and feel right at home.
The moment I opened the Galaxy Map and zoomed out for the first time I knew what I wanted to do in the game: Go out there. So I searched the forums and youtube for some exploration guides and tips on how to get started and equip a ship capable of exploration, and was totally inspired by some of the information, videos and threads I had found: the fact that you could tag systems and planets if you first discovered them, awesome screenshots, pioneers who first made it to the other side of the Galaxy, the Distant Worlds expedition etc.
So I spent my first week in the game earning credits by doing BB missions in my Sidewinder to earn me a Cobra Mk. III, which I then used for some rare trading and bounty hunting. Once I had the credits I outfitted my Cobra for exploration and went on my first short range expedition to the Pleiades nebula. I wanted to know if exploration really was something for me before committing to a longer trip. It was awesome. Approaching the nebula, seing all the different kinds of systems out there, taking beautiful screenshots and even getting some first discoveries on the way. But I wanted to go further, where only very few people had been before, so I returned to the bubble, sold my data for a million credits or so, improved my ship and immediatley left again for NGC 7822. The trip there and back took me a few days and I realised that in order to enjoy exploration I had to mix it up a bit: Take my time to explore some interesting systems thoroughly, take screenshots and enjoy the vastness of space, and just honk and scoop to see how fast I could go. I set myself goals like doing the honk and scoop as efficiently as possible and to stop doing that as soon as it started to feel like a grind.
So when I turned in my data for about 10 million CR this time I had enough to buy an Asp Explorer. I did some more rares trading until I could afford the best FSD and a 6C fuel scoop and off I went core-wards with the intention to not turn around before I'd reach Beagle Point. I'm almost half way there, visited the Great Annihilator and Sag A*, have first discovered ELWs, ringed Water and Ammonia Worlds, Neutron Stars, White Dwarfs, Black Holes, systems with all kinds of interesting constellations and taken some wonderful screenshots. The parts when I'm just honking and scooping I perceive as relaxing, not grinding. Sometimes I have to force myself to refrain from too much detailed scanning, because tagging all these interesting undiscovered worlds is so tempting but would take centuries. I enjoy the feeling of being out there, alone, a long long way of unknown space ahead as well as behind, knowing it will take me weeks, maybe months before I'll be back in the bubble again.
It can be dull, just as hours of trading, mining, bounty hunting, Power Play or whatever activity in game as well as real life can be dull. But I enjoy exploration immensely.
Please excuse my less than stellar English.