Leave the frontier and head out to VY Canis Majoris and take a look at one of the largest known stars - its literally on our doorstep, less than 2,000 LYs distant. From there begin your journey across the Vela Molecular ridge (be careful as there is a wide area of Brown Dwarf sectors out that way so you need to follow a route that has refuelable stars dotted along it).
The NGC 3590 Open Star Cluster sits on the outer rim of the Orion arm. It becomes visible outside your cockpit canopy at around 500 light years distance and is well worth a visit. Follow the Orion rim to the Eta Carina Nebula. When I went during gamma it wasn't very impressive, but looking at the galactic map now it looks like the devs have given it some love and attention.
From Eta Carina, cross the interarm void into the Sagittarius rim. The star density is such that its probably best to have at least a 25LY jump capable ship.
Following the rim back you can use the V945 Scorpii cluster as a reference guide - its a cluster of some of the brightest stars on the map. From there its back across the void, into the Orion arm, visiting the Shapley 1 Wolf-Rayet system on the way home. A round trip of just under 30,000 light years.
For those heading to the core regions don't take the direct route as you'll miss out on some stunning things along the way. The Lagoon nebula hardly gets a mention from explorers but its definitely worth a slight detour. From there its the long haul across to the CL Pismis star cluster embedded within NGC 6357 (there are some permit only stars in there that could be hints to a future FD event).
From there if you're heading galactic core-ward, you'll need to cross the 3kpc - Norma Arm Expanse, the first half of which has a lot of brown dwarfs but thankfully plenty of refuelable stars amongst them. The expanse thins out about halfway across but then you're hit with a wall of stars as you enter the near rim of the 3kpc Expanding arm. Unfortunately anything after the 3kpc arm is playing Russian roulette as the game becomes more and more unstable with broken sectors (FD are aware of them thankfully). If you get stuck in them you won't be able to log on until game support gets to your ticket and moves you. Hopefully this will be fixed in a January patch.
If you've got this far you have got to visit the Greae Phio stellar forge - its one of the most impressive sites I've seen. There are also lots of supernova remnants dotted about the outer core regions, the one I visited was 1,200 LYs above the galactic centre - giving impressive views of the sheer amount of stars below you
