I've been thinking about Nightwing a lot lately because of Forever Evil. A lot of his connections in the DCnU aren't clear. After thinking about the love triangle with Starfire and Batgirl I started thinking about what was shown in RHATO. It's kind of vague what he thinks about Jason Todd, Koriand'r and Roy Harper much less what they think of him. Even with one of these relationships shown in other books.
In the first RHATO issue Dick is brought up by Roy who's under the impression that Kori and Jason are dating. Curious to how her ex would handle the news and if Kori knows of their fights he asks Jason. Not appearing to care Jason shrugs saying it doesn't matter since Kori doesn't remember him. When asked by Roy she says she doesn't know Dick and changes the conversation. From what's shown it's hard to say how what Roy feels towards the guy, Kori doesn't seem to care and Jason seems to regard all of his family in a negative light. But things aren't what they appear so let's see if we can shed a little light on the matter.
Starfire and Nightwing
Kori claims that she doesn't remember her past, something Jason repeats but we learn later he doesn't really buy it. She shows no problem recalling her history prior to arriving on Earth but gets angry when she first discussed her time as a slave with Roy saying it was in the past. Despite telling Roy she doesn't remember Dick she nevertheless says "R'ichard" at one point when alone. When she first meets Jason she's reminded of Dick then due to her ship holding some of his clothes admits she knows he (Nightwing) was her lover. Kori seems to view the relationship in a positive light but has moved on although she claims she can't remember his name. Yet in RHATO #17 she refuses to go inside Wayne Manor when Jason invites her in. While inside Dick sees Jason and doesn't seem to be upset that she's there. The reason he gives for not seeing her is that he thinks the people around him suffer thanks to the events of Death of the Family. Jason doesn't think Dick realizes just how great Kori is which seems to irk Dick. He tells Jason to look after her which he agrees to do. So Dick obviously still cares for her.
Later on Tynion introduces then drops a plot point of Kori intentionally making herself forget things due to them being painful. The memories are still there just buried and one of them seems to imply she might have physically hurt Dick. Nothing else is ever mentioned.
Arsenal and Nightwing
This is perhaps the vaguest of the trio since neither mans' current opinion of the other is ever given. Roy has no problem bringing Dick up but it's always to ask how the other two feel about him. In one of Koris' memories it's shown that he teamed up with Kori and Dick before. Comfortable enough to call Dick "boss" back then and follow his lead. In #2 Roy comments that he's effectively being ignored by the superhero community although Lobdell has said that he never saw Dick as the type to freeze him out since he's a nice guy. When the Outlaws come to the Manor in RHATO #17 Dick doesn't see or mention Roy, not even to ask Jason to take care of him too. It's unknown if he's even aware of Roy hanging out with Jason.
Under Tynion Jasons' memory of his first meeting with Roy has him mentioning Dick as Roys' friend before he fell off the wagon. This seems to imply that Dick cut off communication with Roy once his addiction(s?) took hold.
Red Hood and Nightwing
Although this is the one that's shown the most it's by no means fleshed out. While Jason is dismissive of Dick in #1 in #6 it's shown that he has trouble dealing with him. When Jason's healing from his wounds his mind goes to Dick training him as Robin. Feeling that they were competing he wasn't too pleased with Nightwing although he was listening to his advice (not shown in flashback but he says he was.) Jason's visibly upset when he sees Dicks' uniforms in Koris' closet and seems to think he hates him. I say seems because he's not always a reliable narrator especially where his family is concerned. When Damian calls the former Robins into a meeting the two see each other first and have a stand off. Neither is too happy with the other. The art implies Dick attacked first since Jason is poised with his foot still on the ledge then Dick picks on him a couple times. He suggests that Jason needs to redeem himself which is different from what Morrison was doing. Later on during DOTF Dick tells Damian he's the one who called Jason to the manor although neither has anything to really say to the other. Their main focus is Bruce and how his actions affect all of them.
In RHATO #17 the two talk although Dick is noticeable tense although that may be because of DOTF. Jason's more causal but neither seem as attack happy as they were at Damians' meeting. Dick doesn't have any objections to Kori being around Jason and in fact trusts him to make sure she's okay. He's the only one shown at the manor that doesn't rush to Jason after Jokers' attack but it's not known if he left or was trying to avoid Kori. There's also Jasons' time as Wingman in Batman INC. but I never know how much of that is canon.
With Kori it seems like she's more negatively affected than Dick is although both have admitted they care(d) for the other. Roy doesn't seem to mind Dick but neither have gone out of their way to see the other. It's not clear if Dick dropped him as a friend due to his addiction or they just fell out of touch. His relationship with Jason varies based on who the writer is although Dick has come off the worst in terms of behavior.