I hear a lot of musicians complaining about the tunes they are required to play. Yes, I agree some tunes seem "hipper" than others, yet when we blame a lacklustre performance on the material we are playing, we abdicate a lot of our personal responsibility and power. Bill Evans described tunes as "vehicles". In other words, we can inject whatever we are playing with as much life (or death) as we want.
I've probably mentioned this before, but the first time I saw Ray Brown's trio play, they opened with "You Are My Sunshine" with Ray playing the melody. It's probably not the most amazing composition ever, but it sure sounded great when they played it! Sure, they could have played some more obscure original tune, but they started with "Sunshine". Everyone knows that tune, and it got the audience on board IMMEDIATELY.
Even if you're playing tunes that don't include improvisation, do what actors in the theatre do and create "the illusion of the first time". You want to make your performance always sound fresh .
As well as Ray Brown, Sonny Rollins always has played music familiar to all and added the hipness himself! Here's a concert he did in Montreal where he opened with the Dolly Parton hit " Here You Come Again". Sonny sounds great of course, and check out DeJohnette's serious badass shuffle!
In conclusion, if you find yourself disliking a certain tune, find a way to rearrange it, or change what you're playing, or change your attitude to what you're already playing etc. Accept your boredom/frustration with a tune as a challenge, and as a creative person you will find an innovative solution! I look forward to hearing it!