Upgrade From Shared Hosting?

I currently host my site on Bluehost for around $10 a month. But my site is growing and I need more speed. I’d like to upgrade and don’t mind paying more but Bluehost is including a lot of useless stuff that I don’t want like dedicated IP address, SSL etc.

I want everything to remain the same, but I want more resources, CPU time speeds etc. I don’t want a VPS cause I don’t want to mess around with installing and managing a server environment by myself.

I don’t mind switching hosting providers. Can anyone tell me of a service that gives better performance than shared hosting and maintains the same abstraction I get with my current plan? Ideally it should have far fewer domains on it than my shared hosting plan has at the moment.

I checked Godaddy, but their plans is very suspicious. It says it “scales dynamically” across multiple servers, but it’s absurd to think that they can offer this at a low cost of $5 a month. What gives?