Other places near to Koppal city are TB Dam Hospete, the famous Vijayanagara capital Hampi, Anjanaadri Betta - birthplace of Lord Hanuman, Kishkinda, Anegundi which all are within 30 - 35 km radius from Koppal....You can also stay in Koppal for affordable priced hotel rooms as there are no. of lodges available.
There are yet many things that can be done in Koppal like wandering in the city, roaming into local market, going to public playground etc.. and it all depends upon time available for you can spend.
Best time to visit Koppal is from June to February, later as I said in the beginning, mercury level rises upto 40 to 45° Celsius here.
Do visit Koppala once, do visit my native once.