Jeez. I am originally not even from Athens or Georgia originally, and am no "expert" by any means, however I could have come up with a more sensible answer - than suggesting breaking the law by trespass and poaching, and possibly ending up with buckshot getting picked out of your back and butt at the local hospital, or ending up in court paying a citation or jail, unless that is your bag.
Whatever. With respect, it just will not suffice to let this stand as a legitimate answer, in case other sportsmen who don't wish to break the law happen look at this thread in future when there are lots of fine excellent places to go fishing in Athens.
Here is a much more sensible list of 10 - legal - places to fish in Athens.

1. Bear Creek Reservoir - Bear Creek Reservoir is a 505-acre impoundment owned by Upper Oconee Basin Water Authority. The impoundment has limited bank-fishing opportunities. Bank fishing is limited to one designated area on the lake, which might be 50 yards long. There are currently some very good catches being made from Bear Creek. The plus is that there is good and easily accessible parking near the designated area, and it is a reasonably pleasant place to fish.

2. Bell's Lake - Bell's Lake is a privately owned pay lake outside of Watkinsville. The banks are clear all around the lake and you can drive right down to the edge. It costs $5 per day, hours are 8 a.m-6 p.m. and there's a six-fish limit. You can bank launch a small boat, and the cows and their patties are a bonus.
Directions: go to Watkinsville, and from the split of Georgia Highway 15 and U.S. Highway 441 Business (in front of Jittery Joe's), go south on 441 Business to Colham Ferry Road, turn left, then go 0.8 miles to Bell's Lake.

3. Broad River - The Broad River is one of the great untapped fishing resources in the Athens area. For the size of the fishery, it gets a minimum amount of pressure and offers a broad selection of species of fish to target - including the local version of the redeye bass, the Bartram's bass.

4. Crows Lake and Catfish Farm - This is another pay facility, which is located just outside Jefferson. Fishing here is as near a sure thing as you can get, but can get rather pricey, as you pay for your fish by the pound, and there is no catch-and-release of catfish (without paying a premium). The catfish are fed daily, and catching them is automatic. The daily fee is $3, $1 for children 9 and under, and all catfish and bream are $2.20 per pound. Directions: Starting at the Athens By-Pass, on Prince Avenue/Jefferson Road, go north on U.S. Highway 129 for 15 miles, and the lake will be on your right at the intersection of Georgia Highway 11.

5. Commerce Watershed Lake (Commerce Water Supply Lake) - As the name suggests, this lake is part of the Commerce water supply system. Bank access is good and boats without gas motors can be launched. Fishin tends to be hit or miss.
Directions: Take U.S. Highway 441 (Commerce Road) North, cross over Interstate-85, the first road on your left after I-85 is East Ridgeway Road, turn left, and follow this road to Water Plant Road, turn right, and follow the road to the lake.

6. Fort Yargo State Park - Fort Yargo State Park has a 216-acre lake, which in the past has provided excellent fishing. Private boats are permitted and rental boats are available.

7. Lake Herrick, University of Georgia - This lake is located at the intramural fields on College Station Road and is open to the public for fishing at no charge. The lake gets pretty heavy pressure, but has good vehicle access and good access to the water. No private boats are allowed, but there are canoes available for rent to students and university personnel.
Directions: Get on College Station Road, go to intramural fields, enter, and drive to the lake, which is at the far end of the road on the left.

8. Oconee River, Middle - Sort of playing games here with the name, so that both Oconee Rivers can be listed together. The Middle Oconee River has excellent access at Ben Burton Park, which is located on Mitchell Bridge Road, parallel to the bypass on Athens' north side. The river along the park has several shoals, which can be reached from the bank or by wading. The fishing is available to the public during normal park hours (dawn to dusk). The lower end of the park gets serious pressure, but the upper end near the old dam doesn't get nearly as much attention, and some nice river fishing can be had there.

9. Oconee River, North - The North Oconee River is one of the great untapped fishing resources in the area. The construction of the North Oconee River Greenway has opened a section of the river that was previously inaccessible. Access is still spotty, but catching some fish there is just about a given if a little effort is extended. The North Oconee River presents a classic river fishery where small spinner baits can catch a wide assortment of fish.
The best access points are:
North Oconee River Park on Willow Street: There is a bus stop at the park, and the truly urbane fisherman could take the bus to this fishery.
Dudley Park: Dudley Park is about two blocks from downtown, bounded by Oconee Street and South Peter Street.

10. Watson Mill Bridge State Park - This state park has limited fishing resources and gets heavy pressure. Fishing in the river below the dam is probably the most interesting feature of this location. The park can be accessed either by driving north on Georgia Highway 72 (toward Elberton), or north on Georgia Highway 22 from Crawford.

Quoted:
Lake Oconee, Lake Sinclair, Oconee River...all offer good fishing, if you have a boat.  There are lots of small farm ponds everywhere, the trick is finding them and getting permission from the owners.  If you ever want to come to Milledgeville (about 60 miles south), I'll take you fishing...we can take kayaks on the river, or hit Sinclair or Oconee.

Quoted:
I usually just look around on Google Maps

Always wanted to fish that pond right off the Loop between exits 12 and 11...