Mbeya is a city in Tanzania. It's the gateway to Malawi, and the southern access point to Lake Tanganyika.
There are a couple of hotels across from the bus station, popular with those heading to Malawi the next day. Avoid the travel agencies attached, many people have reported scams with transport.
Malawi is your likely destination... there is no transport that goes direct from Mbeya to anywhere beyond the border, so ignore any bus drivers or travel agencies that tell you otherwise... many people pay to get all the way to Mzuzu or even to Lilongwe and are sorely disappointed when they get across the border and find no connecting bus.