Hi,
There are a number of ideas from which you could choose one and make your final project.
Implementing a UART or a USART chip in VHDL/Verilog is a great project. It will not only help you learn about serial communication but also about how sequential circuits are realized using HDLs.
Making a small microprocessor is another great idea. It will give you a thorough experience in microprocessors, memories, handshake protocols, and of course digital design.
If you want to learn a modern technology, study and implement the AMBA bus architecture. It is a good bus architecture by ARM and is being used in many modern RISC-based processors, probably even in the phone you have. It's not difficult once you understand the various signals involved in it.
If you want to work with combinational circuits, then explore arithmetic circuits: adders, floating-point units, multipliers, shifters, etc. It is a vast and deep ocean of VLSI circuits and an ongoing field of research.
If you want to try analog design, then implementing opamps, PLLs or data converters like ADCs or DACs will be a good option.
Hope I have given you enough choices. Just make sure you learn something out of the project you choose and not just complete it for the sake of doing it.
All the very best!