I would definitely talk to your doctor about the blood pressure before you start anything strenuous or if you're planning on taking up like weights and stuff. But in the meantime walking is a generally safe activity. The best thing for lowering blood pressure and improving cardio fitness is "LSD" or "long slow distance" so going for long walks is really good. But defintely talk it over with your dr as well.

Also, talking about it to your dr to see if you need it to be controlled with meds? Your weight doesn't seem to be a huge issue and so it might be linked to something else. You coudl also try cutting out excess sodium from your diet as that can affect blood pressure. Does it run in your family?