A good weekend trip is defined by the travel time as much as the destination — anything past four hours each way starts eating into the trip itself.
From Delhi, Rishikesh and Neemrana both fit comfortably into two days. From Mumbai and Pune, the hill towns around Lonavala and Mahabaleshwar are the standard escape. From Bangalore, Coorg is a stretch for a single weekend but rewarding if you leave early Saturday.
Book accommodation ahead for weekend getaways specifically — these routes fill up fast precisely because they work so well.