As far as I know altitude should not make that difference. As you indicate exercise is the best way to lower blood pressure - but walking may not be enough!!. Unless you are elderly, say over 70 or so, I would suggest a tougher workout.
To be effective you need to get your pulse (heart) rate up to your age-based (safe) level. That's about 85% of 220 minus your age; so if your are 50 that's 0.85x(220-50), or 145 bpm. You need that for 12-15 minutes, daily, or better twice a day. After it you need to be sweating and feel drained right out!!.
Of course if you have a heart condition or any concern at all you should talk to your GP first!
People don't understand that blood pressure is HARD to control once you get past decent exercise and decent diet (ie low salt). Medication has many side effects, so if you can do the diet and proper exercise thing you are really better off. Even if it does not fully lower your BP it will help, and you will need LESS medication which means LESS side effects, and you feel better.
I have a friend who, when I mentioned exercise said "Ok, I'll get a Wii (Nintendo) exercise game". The latest fad - you can imagine how long that lasted. It's like the late night TV exercise machines they sell. It's not getting the machine. It's proper motivation from WITHIN that's required, and you can't buy that!!
All I can say is the harder you exercise the more you will like it, and the more you will feel it doing you good.
Beefy in Oz.