Everyone needs a pump. A mini pump will still be a lighter and much cheaper option than CO2 cartridges. And even if you take a CO2 inflator to speed up getting back on the road, you may still need a fall-back option to get you home if you get multiple flats.
A mini pump should be pocketable or attachable unobtrusively beside your bottle cage — that way it's always attached to your bike and ready for action when the inevitable happens.
The pump usually clicks into the mount and is secured with a Velcro and/or a rubber strap. It is likely to get mucky if you keep it here though, particularly in the wet or if you're headed towards unpaved roads.
Protection of the valve connector and sealing between barrel and handle are important considerations if you plan to use the frame mount.
Some are so mini that they will fit into a saddle pack, although pump stroke and efficiency are likely to suffer in such a short pump.
For pre-ride inflation, we would always recommend a good track pump with a gauge.