Hi GeeDee,

Thanks for your question.

Hiking and trekking possibilities are the best in the North around the City of Chiang Mai. You can take a train, bus or plane from Bangkok to get there (with train being the best experience).
Chiang Mai is really a lovely city and indeed very safe. For trekking I would recommend you to get a guide on your trip (for obvious safety reasons) or just join a group of other people.

If you want to book a budget hotel I could recommend the Chiang Mai Gate Hotel which offers reasonable prices and clean rooms. From there it's very easy really, there are plenty of small travel agents around you can arrange your trekking with.

Please let me know if I can help you with any further advice.

Cheers and good luck!