closeup for flower pics and zoom for birds/wildlife

I've been taking pictures for years but recently started using an older digital camera with manual controls (5 megapixels and 3X zoom). I've experimented with manual settings for Christmas lights, foggy days and closeup of flowers. I'vd done some decent flower closeups with my point and shoot (Fugifilm FinePix F450) over the years but want to step up to a camera with more zoom capabilities without sacrificing the macro ability.  I do not want to buy a DSLR and deal with different lenses.

Thanks for any helpful insight