Badami, Aihole and Pattadakal make a doable circuit.
Also consider the Mahakuta and Banashanhari temples.
Assuming you are basing at Badami, you can make a short detour to Mahahuta on the way to Pattadakal from Badami. Similarly, Banashankari can be covered on the way back from the Pattadakal to Badami.
The Badami to Pattadakal distance is about 22km. If you make a dtour via Mahakuta, It's a couple of km more.
Banshankari to Pattadakal distance is about 17k and Banshhankari to Badami distance is about 5km.
Also note, the Badami Railway station is about 5km north of the Badami Caves site.
Aihole is 15km north of Pattadakal.
Hampi at a distance of 150km southeast of Badami is another major destination around this circuit.
The Virupaksha Temple of Pattadakal signifies the high watermark of the Early Chalykyan architecture. This temple was built in commemoration to the victory of the Chalykyas over the Pallavas of the Kanchipuram.
Galaganatha Temple dedicated to lord Shiva is a compact yet strikingly unique temple in Pattadakal. The most striking part of the Galaganatha Temple is its dexterously executed tower and the fluted final atop. Most likely the Galaganatha Temple was built around 750 CE during the regime of the early Chalukya king Vikramaditya II.
Golgumbaz Express (Train Number 6535 / 6536) is a tri-weekly express train between Solapur and Bangalore( Yesvantpur Junction). In the Yesvantpur to Solapur route it is called Solapur Express and in the return route it is called Golgumbaz Express.
Chalukya Express connects Mumbai with Bangalore. That is Chalukya Express operates between Yesvantpur Junction in Bangalore and Dadar in Mumbai.The train is named so because its route passes is right through the erstwhile Chalukya Empire heartland.
Well, this is piece for those of you who are new to the concepts of Hinduism. To that extend this is an oversimplified narration to make the understanding easier. For those who are keen to know more, the scope and resources are endless. So that's a disclaimer to begin with! Though it is referred with a single common name , Hinduism, it is in fact a conglomeration of many sects, sub sects , often with its own pantheons, beliefs and religious practices. Unlike many religions, Hinduism doesn't have definite a founder. The religion practically 'evolved' over 4000 years or so into its present form.
Lord Shiva slaying Andhakasura, the blind demon, is a popular mythological theme carved on many Shiva Temples. At Pattadakal you can see a giant image in the south side of the Galaganatha Temple. The story goes like this. While in the mount Mandhara a baby was born to Parvati and Shiva. Shiva was in a meditating posture and Parvati closed his eyes mischievously from behind. The boy appeared out of Parvati's sweat. Shiva explains to Parvati that since his eyes were closed, the baby was born blind and calls him Andhaka (the blind). Since he posed devilish qualities he was called Andhakasura (the blind demon ).