After some investigation, I’ve settled on my replacement for Google Reader, InoReader. It authenticates and synchronises with your existing Google account and reader subscriptions (although I had to go through and mark some subscriptions to unread which I had already read). To make things easier, get your existing google reader to 0, or simply mark all as read when you make the switch.
Note along the way I tried Feedly, but I couldn’t get comfortable with the interface and gave up in the end. However I think other people will quite like it, and it does have a lot of platform support.
For larger articles that I want to read on my tablet or archive, I use Pocket. I find this much better than “starring” articles.
These are just my personal preferences, there are hundreds of options out there and they all depend on how you consume RSS feeds.