The Alamosa area is an agricultural area. The Dunes are a great place to visit, with a small warning--hiking in loose sand is exhausting. You can get some great photos around the perimeter, but if you want to hike in, be careful.
If you have time to drive some distance, you won't be very far form the San Juan mountain range in the southwest of the stste. Its the most dramatic range in the Colorado rockies. Alamosa to Durango to Montrose to Salida to Alamoso forms a square that will give some amazing mountain views. There are some other shorter options like Alamosa to South Fork over Slumgullion Pass to Lake City to Gunnison, over Monarch Pass to Salida and then back down to Alamosa is much shorter and still has some great views. My favorite section is from Creede to Slumgullion pass where you have lots of open fields and meadows at 11,000 feet.
That skips 550 (the "million dollar highway") which is the most dramatic, but also very heavily trafficked by tourists driving 20 miles an hour.
A little closer is to drive south to Antonito, and take the narrow gauge train to Chama New Mexico. It goes through some stunning scenery and you don't have to drive just enjoy the views and take pictures. If the cost of the train is too much (it has gotten pricey) you can track the same route (mostly) by driving Route 17 to Chama.
There are a lot of other great places in Colorado but those are closest to the Alamosa valley. If you want something completely different than the rest of Colorado drive to Gateway. The road to the east of Gateway and to the south of Gateway (Rt 141) is my favorite ~100 miles of pavement on the planet and absolutely stunning the whole way. But that is quite a distance from Alamosa.