We have been using hankies in place of tissues since my first Plastic Free July. Tissue boxes generally all have some plastic wrapping, whether it be around the whole box or inside the top.
By using reusable handkerchiefs instead, you are not only preventing plastic waste, you are preventing lots of paper waste. My husband went through so many tissues before we made the switch, I used to joke he killed a forest of trees in tissues. And handkerchiefs are so much easier on your nose, they really do a better job than tissues.
We got our hankies here, and we keep them in a little basket I found at Goodwill.
If you aren't familiar with Plastic Free July, take a look at this post. Basically, it's a month-long challenge to reduce the amount of disposable plastic you use. It's a great starting point if you just want to give cutting out disposable plastic a try.
My first Plastic Free July was in 2013(!), and this month I'd like to highlight some of the things I do to reduce my plastic use, and some struggles. Many things are part of my routine at this point (buying in bulk, refusing plastic silverware, etc.), but I am not perfect, and I always find this challenge to be a good time to refocus and look at what trash I am actually producing.