How to say NO without offending ?

Favors are not part of the Project Charter (PC) and Project Management Plan (PMP). They are more a personal person-to-person request. If you can handle the request, such as can you provide a photograph of the Governor visiting the project site. It may build some good will but do not increase any risk to the project. Sometimes NO is the most concise and expeditious answer to a favor. If needed, NO can be followed by indicating the request it is outside the PC and PMP. If the request for favor continues, the PMP describes the process and justification documentation for changing the project requirements.

Be professional about it, but at the end of the day, you cannot control if someone else gets offended.

Be professional
Be respectful
Do the right thing
Be consistent

I would add local culture

A favor may technically be a change request. Run the request through the integrated change control process for proper evaluation. Identify the risks, pros, the cons, and the impacts to the project. If in the end the decision is a "NO", present the facts and the reasons why it is a "NO".

It may also be a "YES' in the end after acquiring all the facts but all risks, impacts, pros and cons will be recognized and will be taken into account.

Hi agree with Joseph, a favour can be considered a change request, therefore it should be run through the Integrated Change Control process.

Sometimes, as a PM, you will be so involved in the project that you might loose the reality of what's happening around you, you might feel the pressure and agree to go ahead doing a really costly favour only because you feel the necessity of keeping the stakeholder happy.

Analyse the situation, identify possible risks and what the favour would mean for your company in terms of budget, schedule etc and then provide the outcome to the stakeholder.

Be professional, follow the processes and explain the reason of your decision with confidence.