I always have to ask to go to someone else's town because whenever I try and host at mine I get the blue resetti screen, but with no code, just a message saying an error had occurred. I can visit other towns with no problem. This makes me think I don't have a weak connection as has been suggested before.

Is anyone able to shed any light on this?

You likely have a built-in firewall enabled on your router preventing others from connecting with you easily. If you know someone who can manage your router settings, or if you're the only one, then I would recommend setting your 3DS to have a Static IP. Then you can put it through DMZ which will avoid having to disable your router firewall. (further steps here)

Let us know your results!

Thanks, I didn't even know that was a thing! I'll let you know how that goes when I have time to sort it out tomorrow