Pretty much everywhere I go I have a basic backpack, not for nappies or stuff I just find it's generally good to have a bag on me, but If I'm going to take any nappies or other stuff it will go in there.
I recently saw
this bag on amazon and was really tempted. I dont like the top handles and don't need the stroller straps which both make it quite obvious it's a nappy bag but I do love the idea of an integrated bottle warmer and the USB port on the side (though I'd want to know it is covered for bad weather.) also the main compartment may have multi pockets but they don't look all that big on the sides and I'd want space for spare changes of cloth inserts which are much bigger than the few baby nappies they have pictured. The wet wipe pocket is also a nice touch but it would be nice to have a warming element in that as well like the bottle one since I use reusable wipes and they can get very cold this time of year.