Designing new computer languages is a major research interest for computer scientists. One of the main concerns in this subject is designing languages that are user-friendly and practical. A project on language design could develop an entirely new language or make changes to an existing one. For example, you could build a language that uses written commands (e.g. "if" and "then") by writing a series of "yes" or "no" commands ("bits") that correspond to keyboard strokes. Alternatively, you could write a research project that explains how an existing language (e.g. c++) translates keyboard strokes into binary commands. In this project, you would use a translator to convert from c++ commands to binary, while drawing on other research papers to describe the conversion works.
Software design has always been popular with computer scientists. Using object-oriented languages, computer scientists can design user-friendly programs for use by non-experts. There are many angles you can take if you want to do a project on software. If you want to design a totally novel piece of software, work with a supervisor who has some experience in software development. New software is often written in C, Visual Basic, Java or c++. To design a useful program, you need to find a computing problem that people struggle with, and come up with, a solution to that problem. For example, you could attempt to develop a calculator that factors large numbers whenever the user enters them into a document.
Artificial intelligence (AI) is a hot topic in computer science. AI has theoretical and practical value. On the one hand, AI can be used to design robots that perform useful functions (e.g. manufacturing) without the need for human guidance. On the other hand, AI programs can (potentially) answer many questions about the meaning of consciousness. A project on AI could tackle the practical or theoretical aspects of the subject or even a mix of both. A practical project would develop a set of algorithms that instruct a computer to deal with variables intelligently. For example, you could write a script that tells the computer to guess the user's preferences based on the programs they access most frequently. A theoretical project, on the other hand, would deal with more philosophical questions. For example, you could write a research paper on the question of whether computer sentience is possible, citing academic journals, as well as published code.
Many computer science students do work with physical models. Physical models (e.g. models of weather conditions or human body parts) involve extensive math, making them perfect for computer scientists, who often enjoy challenging work. A project on physical models could, for example, create a graphical simulator where the user enters wind speed and precipitation levels, and the computer generates an graphics of the rain falling at the appropriate angle. This project could be written using an object-oriented programming language; the key technical challenge would be to determine an equation that models the effect of wind speed and rain volume on the angle of rainfall.