Malacca (Malay: Melaka) is a city in Malaysia. It's very artsy and kind of the hippie central of Malaysia.
North or South towards Kuala Lumpur, Singapore
The motorway is quite far outside of the city and the public transport can be unbelievable inefficient. It can easily take you 2-3 hours to leave the city. First you have to get to the main bus station, i.e. by the local bus from Dutch square. From there, find the bus that goes to the Zoo and take it to the last station. You are now on the main road that leaves the city. It's probably possible to hitchhike there already, but cars are fast and won't know where you are going. It's about 30 minutes walking to a huge toll gate at the motorway entrance, which makes an excellent hitchhiking spot and you are likely to get a direct lift to KL or the Singaporean border from here.
If your driver just passes Malacca, have them drop you at the motorway exit, walk to the toll gate and try to find a lift from there as far as possible in direction of the city centre. Going there by bus will take a long time and taxis are expensive.