I'm married so daytime dates work best for me.  What's a solid weekly-excuse for being away?

But I was in a very nasty near fatal car accident about 18 months back and still have several outstanding medical issues so they are used to me having a lot of doctors apointments

I'm in construction, so there are various jobsites to visit and job meetings to attend.  Also we bid work that has to be viewed first, so there's a good reason to be out.  Finally, it's always a good idea to have some lunch with a client, and who cares if the lunch runs a long time?

On the other hand, if you are in a business where you are pretty much expected to be chained to your desk, that is a problem, but think about volunteering to go to conferences and symposia to improve your skills.  No one notices if you get back from lunch a little late.

I used to hobby during the work week all the time when I was married and had kids around the house, but now I'm divorced and the kids are grown up, so I live for the weekend and hobby then.

The biggest hassle is the cell phone.  The office expects to be able to reach you wherever and whenever, so you might have to leave it on and be prepared for some coitius interuptus should it start to beep.

Good advice already.  Do not become predictable.  If you are normally in the office 9-5, it's a problem.  
Taking a long lunch every Wednesday makes it easy to track you.  Gradually start breaking the schedule.
My former job required trips off site to pick up materials but even that was not long enough for a meeting.  
Taking up power walking on lunch makes it harder to see when you're gone.  
Some folks join a gym...  but you'd better go there sometimes.
You've got to come up with things which make sense for your life.  
Sometimes, a shopping bag with a few items from the discount store can deflect discussions of where you've been.  
skb

Only you know what can be made plausible...

the library and sometimes forget to turn it back on.

So right my phone will not work in the super market...  a place you'd actually want to use it.  I've noticed a phone in the belt case can't be heard (or reached) under a winter coat strapped in my a seat belt.  

So much depends on what out of the office your position permits.  You don't want to abuse it...  but flex hours might be used to advantage.  With the emphasis on health...  I could see power walking / jogging but varying routes & not on the same day each time.  
skb

I enjoy taking long rides on the Harley.  Darn, I just can't hear that cell phone while riding.

evening work obligation.  You are correct in that you need to vary your habits, being too routine and then having a change can arouse curious folks, especially if you come back to the office with a big smile on your face.