I would try to analyze and solve one or more of the problems published on Kaggle Competitions (https://www.kaggle.com/competitions). Note that the competitions are grouped by their expected complexity, from
101 (bottom of the list) to
Featured (top of the list). A color-coded vertical band is a visual guideline for grouping. You can assess time you could spend on a project by adjusting the expected length of corresponding competition, based on your skills and experience.
A number of data science project ideas can be found by browsing the following
Coursolve webpage: https://www.coursolve.org/browse-needs?query=Data%20Science.
If you have skills and desire to work on a real data science project, focused on social impacts, visit
DataKind projects page: http://www.datakind.org/projects. More projects with social impacts focus can be found at
Data Science for Social Good fellowship webpage: http://dssg.io/projects.
Science Project Ideas page at
My NASA Data site looks like another place to visit for inspiration: http://mynasadata.larc.nasa.gov/804-2.
If you would like to use open data, this long list of applications on
Data.gov can provide you with some interesting data science project ideas: http://www.data.gov/applications.