Depending on how long your pump is, and what you use the bike for, an unobtrusive location for the pump is under a longitudinal rail of the rack. Depending on how long your rack is, you might even be able to fit one of the shorter Zefal HPX pumps; they come in four lengths, the longer the more desirable but even the shortest one is a powerhouse compared to most mini-pumps -- there's no substitute for cubic inches of air. This works on tour if your panniers clip onto the lower rails of the rack, and your rack top bag doesn't droop over the edges of the rack, so you can get the pump out.
Here is a vertical mounting to the leg of a rack on one of my bikes.
This doesn't work too well if you use panniers, but I mostly use wire mesh pannier baskets (made by the Dutch Basel company), which leave access to the pump if not free at least visible so you don't scratch your hands extracting it. The pump is an SKS.
Below is my present pump attachment solution. The bottle is a Nathan which comes with rubber diaper, essential for preventing rattles; it's other convenience is that you sip from the top with the bottle upright instead of having to tilt it above your head.
Some Topeak pumps come with a handy bracket which fits under the bottle cage anywhere your bike has sockets, with the pump mounting in the angle of the tube and the cage, instantly accessible. Topeak also sells the bracket separately.
The higher black band is a velcro strap I fitted for additional security, with the end of the velcro hidden under the water bottle: without undoing the velcro all the way, the pump doesn't come out of the clip. The Topeak Peak DX in the clip was the best of the mini pumps by rigorous professional engineering test roundabout fifteen years ago.
Good luck with finding a solution that works for you.