Mysore City is located in the middle of a large tourism hotspot in South India. Also it's pretty close the tourism attractions of Kerala and Tamilnadu.
You can easily use Mysore as the springboard to explore the neighbouring districts and states. Be it Coorg, Wayanad or Nilgiris , Mysore sits in a vantage point to access them all.
Take a look at the map of Mysore districts surroundings.
Madikeri and Coorg area (west of Mysore) :
Coorg district (with Madikeri ,its district capital ) located west of Mysore is popular tourist hub by itself. Coorg region is also a day trip destination from Mysore.
Tibetan settlement Bylakuppe is one its kind of place in this part of the country, further up Nisargadhama island is a popular picnic destination.
Madikeri town, the headquarters of Coorg too has numerous attractions.
West of Madikeri , about 45km from Madikeri town is Talakaveri and Bhagamandala. Talakaveri is the fountainhead of Kaveri river in the western ghats.There are some stunning views of the rolling western ghats on the way.
On the southern fringes of Coorg district is Nagarhole, a very popular national park and Irippu falls on the fringes. So is Dubare Elephant Camp, 30km east of Madikeri town and 100km west of Mysore. All these can make a ideal theme for an excursion from Mysore city as well as your base in Coorg.
The distance from Mysore to Madikeri is about 120 km. That means about 3-4 hours travel by road.To that extend it is a very busy trip from Mysore, if you are thinking for returning to Mysore on the same day from Madikeri.
Kukke Subramanya and Dharmastala are important pilgrimage centers near Mysore. Mysore to Kukke Subramanya is shorter by the Bisle Ghat route (about 170km). However a more drive-able route is via Madikeri (about 200km)
Towards Ooty(south of Mysore):
While a combination of Bandipur (National Park) and Himavad Gopalaswamy Betta is doable day trip from Mysore, further far destinations like Ooty, Masinagudi, Coonoor etc are destinations that needs many days to explore.
Towards Wayanad(southwest of Mysore):
Deep south west, after crossing to Kerala state, about 140km from Mysore is the Wayanad region, nestled in the Western Ghats known for its natural beauty. Mysore to Wayanad route passes through many popular day trip attractions from Mysore (see Mysore to Wayanad driving directions).
Kabini River and Nagarhole National Park too are located southwest of Mysore.
Mysore is the ideal gateway to the legendary Kabini Jungle Lodge and many resorts Orange County, Bison Resort, Serai Kabini, Warterwoods etc located on the Wayanad-Mysore boarder region.
Towards South Kerala (south of Mysore):
South Kerala cities like Cochin (Ernakulam), Trivandrum (Thiruvananthapuram), Alleppey (Alappuzha) are connected by long distance bus connections from Mysore.
Towards North Kerala (West of Mysore):
North Kerala (Malabar region) cities like Kasragod,Kannur,Calicut etc are connected by frequent bus services from Mysore. Also there are a few train connections to reach the northern cities of Kerala.
Towards Hassan, Chikmagalur and Shimoga (northwest of Mysore)
A highly popular day trip from Mysore is Belur, Halebid and if you are willing for a trek, Shravanabelagola.
While the first two are popular tourist attractions for its dexterously carved Hoysala temples, Shravanabelagola is a very important Jain pilgrimage center.
The 17 meters (55 feet) tall Gomateshwara ( or Bahubali ) statue at the hilltop is considered as one of the largest monolithic statues in the world.
Mysore to Belur is some 150km. Halebid is another 18km northeast of Belur. Shravanabelagola is around 85km north of Mysore. Head towards Hunsur from Mysore. After Bilikere turn right towards Hassan. From Hassan you can head for Belur, Halebid and Shravanabelagola.
The region around Hassan and Chikmaglur is the Hoysala hotspot. Some are phenomenally popular tourism attractions (like Belur & Halebid), while the rest are equally sought after by those with curiosity in medieval history and ancient architecture.
Beyond Belur is Chikmaglur , a popular hill station with numerous coffee plantations. Further north Shimoga is a larger city, gateway for the popular Jog Falls.
Those trekking fan would find ample choices in the Coorg and Chikmagalur regions, thanks to its closeness to the Western Ghats.
Towards Srirangapatna and beyond (north of Mysore)
Srirangapatna is a classic day trip destination from Mysore.
Another popular religious destination in this direction from Mysore is the Vaishnava site, Melkote, that's about 50km from Mysore. On the way to Melkote some 40km north of Mysore is Tonnuru Kere, a popular spot among youngsters looking for some weekend splash.
Those keen on ancient architecture, this region has many Hoysala era soapstone carved temples like the one at Basaralu, Hosaholalu, Kikkeri, Govindanahalli to list a few. These can be covered as day trip from Mysore as well as from Hassan.