For a while now I’ve been using a stainless steel filter disc made by Able (formerly Coava) with my Aeropress.
The nice thing about the Able Disc is that it removes the hassle of needing the paper filters, instead you can just get on with brewing and it cleans up just as easily as the rest of the Aeropress. When I travel for work, I always bring my Aeropress and Porlex grinder and beans so I can brew wherever I am.
Another thing I’ve been doing more recently is brewing with the Aeropress inverted. All you do here is set-up the aeropress upside down with the plunger resting on the counter. Take the filter and screw-top from the aeropress and fill it ~15-20g of freshly ground coffee (touch coarser than espresso grind though in that ball-park will work fine) and fill with just off the boil water.
Because of the inversion you have more control over the brewing time as the liquid isn’t going anywhere. I tend to leave to steep for around a minute, turn it over and plunge it over about ~30secs.
This gives a beautiful clean cup. As with everything experiment with brew times and amounts to your taste.
The Able disc is available at all good coffee suppliers and costs around £13. Definitely recommended if you’ve got an aeropress.