NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) MCD12Q1 dataset contains global rasters of land cover (as defined by the International Geosphere-Biosphere land cover classification).
Classes (1) Evergreen Needleleaf forest; (2) Evergreen Broadleaf forest; (3) Deciduous Needleleaf forest and (4) Deciduous Broadleaf forest may be of interest for your described project.
The data set is available for free download from: http://glcf.umd.edu/data/lc/
You can then open the GeoTIFF files in an open source GIS program such as QGIS, and apply some simple symbology/coloration to create a map showing forest cover for your area of interest.