Lohanjung (2300 metres) can be reached either from Kathgodam or from Haridwar by changing multiple taxis. It is a long journey to say the least but definitely worth it. Once you reach Lohajung there are plenty of budget accommodation within 300-500 INR to consider.
A trek to Brahmatal can be done either solo provided you have camping gear and food of your own, or you can go by a trekking organisation, or by hiring a local guide. It will take roughly 3 days to do the trek, however, the locals do it in less than 12 hours which is only possible for these so called mountain people.