Depends on how big and what features you want!

I was thinking of the closet that is approximately 8x8. Most that I have seen have cement encasement with a steel door.

Phoggie, I know you said you have crawl, but do you have the option of digging a small cellar/basement/safe space in one area of your crawl? That might end up being less $ than a safe room for how often you'll hopefully need it.

One of the least expensive methods for many years was to install a dry septic tank with the top almost at grade level.

You have to make sure it cannot fill with water long term, but they worked for a long time.

I suppose every little bit helps, why else, when it is your only option, do they say to go into a bathroom? With that in mind, and with a limited budget, in my new build we will beef up a bathroom and call it a safe room. This bathroom has no windows and is tucked beside a stairwell and the two shall be reinforced as much as possible: 2x6 walls, simpson ties and hurricane straps everywhere we can place them, 1/2 CDX sheathing, screwed and glued, and a few extra studs and extra bracing. Under the stairwell, aside one wall of the "safe room", we may have room for a cinder block wall. Add an exterior grade door and I'll have a budget "safe room." Less than ideal, better than nothing. My builder wanted my business and will do all of the above, except the cinder block wall, for no additional cost.