For that money you could get Jeep Cherokees/Toytoa Prados/ Older land cruisers and pootrols, but the running costs are going to be big. The Jimny and Vitara are a great option -They are great little cars and surprisingly good off road. They're no rock crawlers in std form but more than fine for the beach. The Jimny's power to weight ratio is similar to a V6 4wd and they weigh bugger all. - Small engines so fuel costs are low, but I think the post 2005 Jimny needs 95 Premium (could be wrong)? If you go the Jimny - get the manual. Its bullet proof.
Vitara is slightly bigger so more luggage space, but also more room for friends to ride along...
You could also look at a Toyota Rav4. Its not a dual range 4x4, but because its so light, with the right tire pressures it should be fine on the beach.
Another option is the 2003 and earlier Kia Sportage - same body on chassis design and with dual range - but bigger engine (2.0L) and less gizmos. Early models has some electrical gremlins. The later ones are softroaders. But they may not meet with your daughter's sense of style.
For that cash you aren't going to get the latest and greatest safety features either - I think Vitara's were 3 star EuroNcap until 2007. 4 stars after.