Don't know where to start. First, you need a car and a better understanding of where Breckenridge is. There is a bus system but for what you want to do you will need a car or make good use of Ubar. Go to your public library and get some guide books on Colorado and Breckenridge. Breckenridge sits on a small river in a box canyon with tall mountains on three sides. There are no easy hiking trails out of Breckenridge. There is a great hiking trail, Mineral Belt trail, in Leadville.

Lots of excellent restaurants but none on water or water views or even much in the way of sunset since you are sitting at the base of 11,000, 12,000 foot mountains. None really specializes in fish because we are a long ways from the ocean.

There are no rivers around Breckenridge suitable for a float trip. Brown canyon to the south might be a possible but most likely by August some of the rafting companies have shut down because of low water. Might find something in Glenwood Spring on the Colorado since it is dammed a lot with the water held back. Also Clear Creek in Idaho Springs might be possible. Fly fishing is possible on the Blue river in and around Dillon about 20 miles from Breck. However, the gondola out of the Breckenridge parking lot should still be running. Marginal views. For scenery the gondolas at Vail would be a better choice.

Good luck ----

There is a good fly fishing outfitter in Silverthorne for fishing in that area which is very good on the Blue and the tail waters of Dillon Dam. Imagine catching a 24" trout in the shadow of the Outlet Shops!!

YOu DO need a car. You will miss a lot of beautiful things to do in the area--and the shuttle to and from DIA isn't all that cheap vis a vis a car rental, IME.

I don't think you have to have a car if you really don't want one. You can hike on the mountain where they ski in August, for example. They have trails open, you can easily get there. And the local bus system goes up Ski Hill Run in summer to Peak 7 and 8. There are some easy hiking trails nearby, I think the local bus system would get you there, but not sure as I've only been there for skiing. Just check some hiking website like Alltrails and then the Breckenridge bus system maps (such as to French Gulch). The Breckenridge resort website shows you terrain status for hiking trails.

I"m not sure what body of water you think this town is on, though. There is a very small manmade pond in the center, but that sure isn't any great water view. The downtown area is full of sports bars. You are not going to get any cheap meal at any of the nicer restaurants, that's for sure, they are pretty expensive IMO, for what you get. Depends what your idea of expensive is, I guess, I think they are. There are some moderate ones, like this Dinners | Relish

I just eat in cheap places when I'm there. For a casual place, I like CB and Potts, it's not quite the bro sports bar atmosphere compared to some others.
https://www.cbpotts.com/menus/breckenridge.php

You can try Southridge Seafood Grill for that, I suppose the trout there would be local, not other stuff of course.
https://www.southridgeseafoodgrill.com/menu

I think you need a car or some tour company for fly fishing. I suppose that might work as they'd have the equipment. There is a tourist office there with lots of info. here's some
https://www.gobreck.com/trip-ideas/o...-breckenridge/

I'm sure there are "tours" like that for other things, you don't have to have a car if you don't really want one, like rafting
https://www.breckenridgewhitewater.com/

Quandry restaurant isn't fancy but has a view of Maggie pond and the mountains. If you can get the right seating at Breckenridge Brewery it too has some nice views. For years, there used to be seafood restaurant in Breck called the Whales Tale, but it's closed. There are some other seafood options, but mostly with an Asian theme.

Despite what someone else said, there are a few hikes in breck:

https://www.gobreck.com/trip-ideas/h...-breckenridge/

I have only done Sawmill, which goes to a reservoir. Just did it a few weeks back. It isn't a difficult one, but doesn't require a car (and we'd done more strenuous ones earlier that week). Peak 8 you can take lifts up and walk down (or walk up). The Peak 8 adventure park has gotten ridiculously expensive, though. Most of the longer/better hikes, though, imho are reachable only by vehicle. There are plenty of hiking options just a few miles out of town. Mostly to the south. Many pass by or end near water features. If you do a google search, you can find them and probably a rating system regarding difficulty. Also, the visitor center used to have options, too.

Well, I HATE the shuttles. They stop halfway there to get "stuff". And then there is the tip and waiting for others to get started, etc. For $250 for 5 days, I think you could get a rental and have more options. Just me.

I would think you would have a parking space with the condo. Some even are covered. There may be a parking area near a trail head, or you park on the side of the road. No big deal.

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Biking: Yes, I have taken the Peak 8 lift up to the top and rode down. Bring bicycle gloves if you have them as switchbacks caused my hands to vibrate in an uncomfortable way with them. Also, IME it is cheaper to rent mountain bikes in town, then take them up with you. They do have them at Peak 8 though.

It depends on a little bit what you mean by biking down the mountain. You can use the lifts to take bikes to the top of certain ski areas and rode down on what is commonly called "single track". It would be unpaved and does required a little technique for riding single track with a fat tire bike. The other approach is the paved bike paths from the top of Vail pass. Some of the bike rental places will haul your bike and you to the top of Vail pass and you can go downhill into Vail -- surprisingly it is not all down hill -- and the other direction all the way to Frisco. From Frisco it is slightly uphill all the way back to Breckenridge following the river.