Hmm - Pitkin county- if you're going to be in the Aspen, Carbondale, Basalt, Glenwood Springs area, there are some great fly shops including http://www.taylorcreek.com/
in Basalt and Aspen and http://www.roaringforkanglers.com/
in Glenwood Springs. Both of these shops are great if you’re fishing the Roaring Fork, Frying Pan etc. and can give you up to the minute advice in terms of conditions and fly patterns that are hot at the moment. If you're new to fly fishing a full or 1/2 day with a guide, especially if you can split the cost with a buddy, might be a a very good investment- you'll learn a ton about reading water and tips on technique. If you do it at the start of your trip and specify that you're looking for a guide to teach-- more than emphasis on the catching- you'll be in great shape for the rest of your trip on your own, especially if you fish with the guide the way you plan to fish on your own. (A guided wade trip if you plan to wade instead of a guided float for example.) But even if you don't book a trip, either shop will give you good advice.
And there are 2 ways to look at your question about flies— anywhere/anytime patterns and specific patterns based on local hatches, time of year and conditions for a specific stream/area.
1. What are some good all around trout patterns for different conditions to have in your box to give you a reasonable shot for trout anytime anywhere?
There are bazillions to choose from in terms of patterns and sizes and different folks will have their favorites. But here are some popular flies that have been proven over the years that are good basics and some good sizes to have in your box and build on that would cover a lot of the spectrum in terms of sizes, profiles and where they fish in the water column. They won't solve the puzzle all the time, but often enough that they'd be worth carrying:
Brown or Tan Elk Hair Caddis size 16 good for any water type, and a good imitation for many caddis hatches. A good go to fly on fast streams.
Royal Wulff or Trude size 14- a good searching fly for fast water, easy to see
Adams Parachute size 16 and 18 – a good mayfly imitation for slower water
Orange Stimulator- size 10- a good stonefly and large caddis imitation
Griffiths Gnat size 20 for when trout are sipping small stuff on top
Green Emergent Sparkle Pupa size 12
Partridge and Orange Soft hackle size 16 (Both of these wets are good searching flies when no hatches are going on, or when something is hatching but the fish don’t seem to be hitting dries.)
Bead head Pheasant tail size 16
Bead Head Gold Ribbed Hares Ear size 14
Bead Head Prince Nymph size 12
Bead head Black Wooly Bugger size 8
Bead Head Olive Woolly Bugger size 10
Muddler Minnow size 8
You can look around and buy these individually or in an assortment that has most of them. Orvis has a deal going on now with an assortment of 20 flies for 9.95 that wouldn’t be a bad selection and has most of these, and the flies are decent in terms of the quality. And any fly shop would have these patterns too, so you can hold off if you have a trip coming up. They’d probably be bit more expensive in a shop, but of higher quality in terms of materials and durability than you'd find from a discount online place.
2. What are the best flies for a specific stream at a specific time and conditions?
This gets back into Mosca’s and AK Jay's excellent advice. If you’re fishing the Frying Pan for example there maybe Mysis Shrimp coming over the dam, and small stuff like Blue Wing Olives hatching, the Roaring Fork might still have some western green drakes popping off, hoppers being blown off the banks, or high flows that make throwing big streamers a better choice. The local shops can give you great up to the minute advice on the hot patterns that have been working based on specific hatches and conditions. When trying to match hatches in a new area it’s always a good idea to get flies that are locally tied (as opposed to Thailand or wherever) since they’ll be proven patterns for the specific streams in terms of size, color, the local “style” of tying imitations may differ based on water type, and the most effective stage of the hatch to fish- nymph, emerger. dun or spinner.
Hope this helps a bit and you have a great trip.