I drew these waves of black and blue this summer at the aquatic center while the girls were in swimming lessons. I was toting a lot of swimming gear so just brought the 5 x 8" lined moleskine and a few pens. This was drawn in black PITT pen, black and blue Sakura microns, and various blue Sakura gellyrolls.
If you are going to doodle or sketch while at kids' activities or the doctors office, consider the actual time you will be able to have your notebook open. PITT and micron pens dry quickly, but gellyrolls take a bit longer. Especially in a humid environment. At first, you will want a table or counter to lean on, but as you get comfy you will be able to lean on the arm of a chair or a hardback novel.
So what holds you back from doing art "on the road" when you have gaps of time? Surprisingly few people look at your art or ask questions about what you are doing. At the gym, a mom asked me if I was an art teacher. At Starbucks, the barrista asked me if I was an artist. At a cafe, a waitress asked me what type of pens I used. It's all been positive. You get into your own little world - in flow.