思{おも}い付{つ}く and 思{おも}い浮{う}かぶ are compound verbs (複合動詞{ふくごうどうし}) - [思{おも}う + 付{つ}く] and [思{おも}う + 浮{う}かぶ].
思{おも}う implies the action that the doer works his/her mind subjectively and emotionally to image/determine/worry/hope/expect/like or love.
日本{にほん}の将来{しょうらい}を思{おも}う。"I think of the future of Japan."
問題{もんだい}ないと思{おも}う。"There should be no problem."
風邪{かぜ}を引{ひ}いたんじゃないかと思{おも}う。"I might/must be a cold."
子{こ}を思{おも}う親心{おやごころ}。"Parental tenderness for children"
彼{かれ}には他{ほか}に思{おも}う人{ひと}がいる。"He has someone in his mind/likes someone else."
付く indicates that someone or something (stain, color, decoration, condition/provision, power, price, name, smell and so on) attaches to the object. [...が] 思{おも}い付{つ}く is used when some (beneficial or good) idea for the doer comes up in his/her mind, especially without a deep consideration. To 思{おも}い付{つ}く something is like the pop sound of the cork stopper when you open the champagne bottle.
いいアイデアが思{おも}い付{つ}いた。"I came up with an idea."
解決策{かいけつさく}が思{おも}い付{つ}かない。"I can't come up with any solution."
思{おも}いつくままに語{かた}る。"I talk things in mind without thinking."
浮{う}かぶ indicates that someone or something rises up gradually or floats somewhere unstable like in the air or on the water. [...が] 思{おも}い浮{う}かぶ is used when the doer comes up with an idea or a certain image/memory/impression from an event. This idea/image/memory/impression can be blurry at first and become clear gradually as you bring the camera into focus on the object.
いいアイデアが思{おも}い浮{う}かんだ。"I came up with an idea (after considering a bit)."
この曲{きょく}を聞{き}いていると、ゴッドファーザーのシーンが思{おも}い浮{う}かぶ。"I can visualize the scene from the God Father while listening to this song."
When 思{おも}い浮{う}かぶ is used in the same situation as 思{おも}い付{つ}く, it gives the impression that you have a little bit of thought before coming up with an idea.