The first three listed below are the usual close-by places that I hike.

Stebbins Cold Canyon
24 miles west of Davis on Highway 128 just before Monticello dam on Lake Berryessa.
There is a five mile loop with 1300 foot climb best down counter-clockwise.
The trail can be too muddy immediately after rain.
And in summer hike it early in the day.
Shorter hikes just go up to the 1500 foot peak and back, or go up the Homestead Trail.
A longer hike adds the difficult Annies Trail loop http://tuleyome.org/trails/anniestrail/

Lagoon Valley Park
22 miles southwest of Davis on Interstate 80.
There are many trails in a compact area. Over time try different trails. Also mountain biking.
The service road to Tower 4 at the southern end is a 45 minute hike with 750 feet of climbing.
Some photos I have taken there.

North Fork American River to Cool
50 miles east and north of Davis on Interstate 80 to Auburn and then 3 miles on Highway 49 to "The Confluence".
A map showing the trails is available from the Auburn State Recreation Area Park office off Highway 49 half way between Auburn and the Confluence.
There are many trails. The 2 and 3/4 hour loop I do really requires a map. It is lovely, mostly in forest - sometimes dense and sometimes open oak woodland.
Start at the Confluence. Head down river (south) five minutes to past the old railway bridge across the river.
Trail then cuts back  (north) and after ten minutes at Training Hill. Take this steep trail south climbing up 1,000 feet.
Take trails south east towards Cool. About 0.4 miles before Cool take the Western States Trail north that further down comes close to Highway 50.
Important - Take the trail marked Shortcut Trail west for 20-30 minutes. This rejoins the more major trail 9also called western states Trail) back down to the river.

Blue Ridge Mountains
50 miles west and north of Davis off Highway 16.
Frog Pond trail is a gentle hike  http://www.yolohiker.org/trails/knoxville/frog/index.html
Blue ridge Trail is a tough hike with 2000+ feet climbing http://www.yolohiker.org/trails/knoxville/blue_n/index.html
There are many trails in this area. Go to http://yolohiker.org/ and click on trail maps.
It's very hot and dry in summer. best to hike at other times.

Mount Diablo from the west (Clayton)
62 miles south from Davis off Mitchell Canyon road which is off Clayton Road.
A map is at the end of the brochure at https://www.parks.ca.gov/?page_id=517#ParkinfoTab4
A nice loop is Mitchell Canyon Fire Road - Meridian Ridge - Donner Creek Fire Road.
A harder though shorter version is Mitchell Canyon Fire Road - Meridian Ridge - Eagle Peak Road.
A longer hike is Eagle Peak Trail - Meridian Ridge - Prospectors Gap Fire trail - North Peak trail - Mt. Diablo Summit - Juniper Trail - Deer Flat Road - Mitchell Canyon Fire Road.

Mount Wittenburg and Sky Trail, Point Reyes National Seashore
82 miles southwest of Davis to Olema and Bear Valley Ranger Station.
For maps and hike descriptions see https://www.nps.gov/pore/planyourvisit/index.htm
A nice 12-mile loop hike is Mount Wittenburg Trail, sidetrip to summit (1407 feet), Sky Trail to Coast Trail, sidetrip to Kelham Beach, Coast trail to Bear Valley trail back to Ranger Station.
The hike can be shortened by dropping off Sky Trail to Bear Valley Trail on Meadow trail, Old Pine Trail or Baldy Trail. Or by returning from Mount Wittenburg on Z Ranch Trail and Horse Trail.
Some photos of a trip there.

Stinson Beach to Muir Woods and return
88 miles southwest of Davis to Stinson Beach. Can park there or better park above Stinson at around 600-700 feet near White Gate.
A short loop takes Dipsea Trail to the Ridge at around 1400 feet then take Lower Old Mine Trail to Pantoll and return to Stinson Beach on Steep Ravine Trail.
A longer loop takes Dipsea Trail to the Ridge at around 1400 feet then continue on Dipsea Trail down to Muir Woods. Hike up Muir Woods and continue to Pantoll via Bootjack and Alpine Trails or via Ben Johnson and Lower Old Mine Trails to Pantoll and then return to Stinson Beach on Steep Ravine Trail.


The Davis area is fantastic for cycling.
A standard 28 mile return easy ride is to Winters via Russell Boulevard bike path, Stevenson Bridge Road and Putah Creek Road.
Another nice short ride is to drive to Winters and take Putah Creek Road west and then go south on Pleasants Valley Road to Cantelow and return.
A nice 50 mile loop takes Russell Boulevard bike path, Stevenson Bridge Road, Sievers, Schroeder, Silveyville, N Merididan, Allendale, Timm, Peaceful Glen, English Hills, Cantelow, Pleasants Valley Road, Putah Creek Road, Stevenson Bridge Road, Russell Boulevard bike path.
The Davis Bike Club has a lot of info. https://davisbikeclub.org/
Including local rides  https://davisbikeclub.org/ride-descriptions/route-maps/local-ride-ideas/
Solano county bike map indicates which roads get less traffic http://www.sta.ca.gov/docManager/1000006736/2016%20BikeLinks%20Map.pdf
Solano best ten rides: http://www.sta.ca.gov/docManager/1000006740/FINAL_Solano%20County%20Top%20Ten%20Bike%20Rides.pdf
The Three valleys loop is great you start in Fairfield.
The  Lake Solano Loop is great,. You can start from Winters.


Closest are
Lagoon Valley Park
Rockville Park
North Fork American River.