Inexpensive Retro Medium Format Options

I'd suggest keep using the 6-twenty, except learn to re-roll the film yoruself to save some money. I've been doing similar with a Kodak Duo (645) and it is a B-L-A-S-T!

If you want a more reliable camera, look into a Rolleicord and get it serviced prior to shooting seriously.

one of the first 6x7 cameras also called" perfect format"
was the Koni-omega.
before that the folders were usually 6 x9 or 6 x 6
and some had masks or flaps for 6x6 or 6x4.5
The did make cameras that resembles 35mm rf cameras.
They were VERY pricey,
Most likely is a 6 x 9 or 6 x 6 folder, easier to use than the classic "art decco" kodak and
and not as valuable. Personally I like the smaller 6 x 6 eye level folders

Well if you need a focus aid and metering of some sort your options are limited. If you can forgo the metering then you have a huge range available. Metering on old cameras are usually not reliable anymore so I would recommend you get a cheap handheld meter. It can also be used for any other meterless cameras you pick up along the way too. Sunny 16 is also not a bad habit to get into.
Anyway, for metered cameras then I think the best choice is a Yashica 124G. They go for crazy money now due to all the hype but they are a decent starter camera. They kind of look retro to the untrained eye but to me, it still looks a little too modern. Get her to try her boyfriends camera for a while to see if she likes the TLR viewing and taking style. However, the lens is actually pretty good so those Lens Baby effects will not really be doable.
For meterless cameras you could go for any of the Japanese TLRs. There are a load of them out there. Or a Rolleicord. These are all cheap and perform very well. Again, they might be too sharp?
Folders are also a good choice. There are a ton of cheap folders out there although the ones with RF are a bit more expensive. For 250 though, I think you could pick up a nice one. Again, the lenses will usually be of high quality...
If you spens the full 250 on a camera, you will get a sharp picture shooter. Most cameras with RFs are also sharp. You need to aim for the really retro, old, "non-pro" cameras of the day to get those Lens Baby effects. These camera are usually limited in their controls (shutter speeds limited, no focus aid, no meter etc) but they are great fun.
Personally I think meterless and RF-less is good. I have great fun with my Zeiss Nettar. It was something like $35 and it produces some *really* beautiful pictures. Wide open, the lens is soft and smooth but still sharp. Stop it down a bit and you have a really sharp lens. Out of all my MF cameras, I think the Nettar has the most character in its lens. It always surprises me with the results. The pop out lens mechanism also never fails to attract attention ;)

i would suggest a Zeiss Ikon Nettar. Its a 6x6 cm MF camera, fully manual. When folded up you can put it in a normal size purse or large coat pocket. Press a little button on top, out pops a small bellows complete with lens, shutter, and aperture adjustements. You can purchase 120 film for it from pro shops, or perhaps from online sites. The fully manual settings force you to carefully consider how you set up each shot, but thats not bad, because it forces you to think about how each setting will affect the image. The going rate for one of these is about $50.

You should certainly be able to get an excellent TLR for less than $250. TLRs are relatively simple cameras, but it's critical that everything is in top optical alignment and mechanical shape. Try to buy a camera where you can test it and have the option of return.

I've only had Mamiyas, Rolleicords, and one Rolleiflex. I'd say don't buy one of these if you're expecting low image quality as your idea of a 'retro' look. These were good cameras with excellent lenses. You may be able to take the edge off the performance by shooting with a large or small aperture, or shooting without a lens hood, if that's what you want.

You may find different older lenses give different 'drawing' of the image. Tessars give a scary-sharp center and a softer corner image when used at large apertures, but you lose the peripheral softness by maybe f/8. Triplets are not as highly corrected and have softer corners, but I have almost no experience with them. The early 1950s Rolleicords like the III were supplied with either a Xenar (a tessar type) or the less expensive Triotar (a triplet).

Mamiya TLRs sell for next to nothing now. They are good cameras. They're quite bulky, but they have a straight film path. A couple of their lenses have tessar design, if you like tessars.

here's a pic of the nifty Zeiss Ikon Nettar ready for action...

If you want a Zeiss try a regular Ikonta (not Super). They look great. Or you might like the Russian copy Iskra or Mockba.

But I think your daughter would like an Agfa Billy folding camera. It has some art deco on it and a decent lens that should make the type pictures she likes from your Kodak 620. Another good choice would be one of the non-RF Bessas.

I've been using a non-RF Bessa (c.1937) for the past 2-3 weeks, and wouldn't suggest it to a beginner. It's very slow to use. You have to remember to set f-stop, set shutter speed, and remember to wind the film each time. I also question if a beginnner used to a digital camera is going to like scale focussing. While I love my Bessa, it is very slow and the ergonomics aren't very good. The Mess Ikonta might work. It at least has a rangefinder.

Kent in SD

I have a Kodak Six-20 that you can have if you want it. It's not great to look at but it works well. I did a post on it a while back. http://photo.net/classic-cameras-forum/00X4UV Email me if you want it. I would highly recommend re-spooling 120 film onto 620 spools though, it will save you a bundle in film and it is easy to do.