First of all this is from someone who is a big Sony fanboy more or less.
Sony needs to keep manufacturing the PS3 forever so that at some point it can achieve profitability. A new home console any time soon isn't in their best interest as it will be more expensive than the PS3 is now. What they need is more reason for people to purchase PS3's forever. My answer to the solution is convergence. This generation has proved that Sony cannot handle the development for two systems simultaneously. The long software droughts on the PS3 and PSP only help to illustrate my point.
Make the next PSP more or less your last system. Pop a slightly gimped cell in there so as game development can assume concurrently with PS3 and PSP titles. Focus on interoperability. There should be no difference between the two versions except graphics (kinda like the psp downloads on blu-rays). You should be able to leave your house while playing the same game you were playing on your PS3. The PSP, despite lackluster software sales, has been a profitable venture for Sony. I dont think I need to tell anyone here how much money the PS3 has eaten.
Improving the PSP.
Keep the Go's form similar. If it had a touchscreen you wouldn't even need to open it up for anything but gaming that works best with tactile feedback controls making it the size of an iphone. Most people wouldn't probably even care to unless they wanted to play core games.
Peripherals. None needed. They all come on board this time. Camera's, mics, gps, accelorometers, and touch screens are cheap to purchase and incorporate without adding much cost to the machine but tons of flexibility as far as getting games developed concurrently to their platform. I could see Sony lowering even further their dev cost much like they did to help bring about more PSP software with it's big brother after a few years adding value to both platforms especially Nu PSP.
Go big on the browser. Mozilla or Chrome. Nintendo has Opera(which i think it would have been better if bundled free on DS) and Apple has safari. Sony needs to compete effectively and the touchscreen would give you better control options than a gamepad. I just don't know that they have it in them and they should consult outside help. Having a good browser would make users spend more time and hopefully money via your machine.
If the increase from the Go in PSN was worth even the low penetration of the machine in a year and a half or two they might be able to relase this new device at 259 retail point and still make it slightly profitable because of it's mostly simple hardware and the ability to capitalize on the new "i-tunes" like service that they should've had in 2005. PS3 becomes more relevant as time passes because you can take it anywhere.
I think Sony has great potential as a convergence company. They already handle lots ip,software, and hardware. If they just brought them together and leveraged the marketing for them to increase synergy between them they might find far better success(ex. Uncharted: the movie launches just before U3(Pepsi cans yes plz) featuring new music from artists on the Sony Label which all of course helps PSP/PS3 or are advertised concurrently with. or PSP advertisments that could also advertise the ease and fun of gathering new Sony content be it movies or music on this new service). I don't really think Sony has the ability to do so.
PS3 could then ride the Nu PSP's success to a larger install base and hopefully someday get those PS1 like numbers and all that money wouldn't have been completely wasted. And Sony had better Hurry up. Apple is getting serious. I give them 1.5 years until their hiring for AAA game designers starts to pay off.
In short it costs less to make a better PSP than PS3. The success of the PSP was more profitable than the PS3. Convergence products work best on the go anyway.