The key idea behind するのに is the idea of purpose. It has a different, more specific meaning than "することについては".
Don't think of するのに as a set phrase because it isn't - think of it as the purpose marker に, except the の is added to convert a preceding verb in する form back to a noun. As such, the する or の may not always be there.
Most of the time, (するの)に and (する)には can be used interchangeably. Again, するの is bracketed because they are not always needed if the preceding word is already a suitable noun (as you will see in some of the examples below).
Here are the four main uses of these purpose markers that I could think of, with some example sentences:
- To describe a use of an item
- 電子レンジはご飯を温めるのに使います。(The microwave is used to heat up meals.)
- 私は通勤するのにこのバイクを使います。(I use this bike to commute.)
- To evaluate something for a given purpose
- この本は英語を勉強するのにとてもいいです。 (This book is very good for studying English.)
- 彼は君のプロジェクトを完成するのにかなり役に立つと思う。(I believe he will be a big help for you to finish your project).
- これは一人で食べるには多すぎる。(There's too much food for one person.)
- To state requirement(s) for a given purpose
- おにぎりを作るにはおいしいご飯が必要です。(To make onigiri, good rice is needed.)
- おにぎりを食べるのにスプーンは要りません。(You don't need a spoon to eat onigiri.)
- To state costs in resources for a given purpose
- この電車に乗るには3000円がかかります。(It costs 3000 yen to board this train.)
- 注文を決めるのに1時間もかかった。(It took me a whole hour to decide on what to order.)
A rule of thumb for choosing between のに and には is that のに is usually used for personal or individual contexts, while には is usually used for general statements. には also tends to place emphasis on what comes after while のに tends to be more neutral. You may have noticed these in the examples above.
For your example sentence, 連絡 is repeated and the meaning of the sentence is not very clear to me. But here are some options you could go with:
- 連絡するにはどうすればいいですか。(What should I do to contact you?)
- 連絡するにはどの番号へ電話をかけばいいですか。(What number should I call to contact you?)
- 連絡するのにいい時間帯とかありますか。(When is the best time of the day to contact you?)
Note that のに/には should be replaced with ために/ためには if the purpose is the clear topic. For example, 日本語を勉強するために日本に来た。